Geometry

Problem 3301

Find the angle measures: $3x^{\circ}=57^{\circ}$ and $(76-x)^{\circ}=$ (Type whole numbers.)

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Problem 3302

A rectangular garden is 8 ft longer than its width and has an area of 345 ft². Find its dimensions (width and length).

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Problem 3303

Sketch a figure where $\overrightarrow{\mathrm{ST}}$ bisects right $\angle \mathrm{PSQ}$ . Explain and perform the construction.

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Problem 3304

Sketch the figure where $\overrightarrow{S T}$ bisects right $\angle P S Q$ . What’s the first step? A, B, C, or D?

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Problem 3305

Is constructing an angle bisector like constructing a perpendicular bisector? Choose the correct answer below.

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Problem 3306

Solve for $x$ and find the measures of angles $x+11$ and $3x-31$ given they are congruent.

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Problem 3307

Calculate the area of a circle with radius 20 units. Use the formula with $\pi$ .

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Problem 3308

Construct the bisector of $\angle A$ . This forms two angles whose measure is $\frac{1}{2} m \angle A$ . Then construct the bisector of one of the resulting angles to form an angle whose measure is $\frac{1}{4} m \angle A$ .

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Problem 3309

Divide the line segment $\overline{P Q}$ into four equal parts using a compass and straightedge. Choose the correct method.

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Problem 3310

How to construct a $45^{\circ}$ angle? Choose the correct method from the options provided.

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Problem 3311

Construct a $45^{\circ}$ angle using one of the methods below. Choose A, B, C, or D.

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Problem 3312

A triangle with a perimeter of 24 m has equal sides. What is the length of one side?

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Problem 3313

Find the length of one side of a square with a perimeter of $12 \mathrm{~m}$ .

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Problem 3314

Graph the equation $y=3x-2$ , find the y-intercept and another point, then draw the line through them.

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Problem 3315

Find the missing side length of a figure with a perimeter of $41 \mathrm{~cm}$ , given sides $10 \mathrm{~cm}$ , $14 \mathrm{~cm}$ , and $1 \mathrm{~cm}$ .

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Problem 3316

Find the length of one side of a regular pentagon with a perimeter of $20 \mathrm{~cm}$ . What is the length in $\mathrm{cm}$ ?

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Problem 3317

A regular pentagon has a perimeter of $20 \mathrm{~cm}$ . Find the length of one side in $\mathrm{cm}$ .

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Problem 3318

Find the missing side of a square with a perimeter of $26 \mathrm{~m}$ . Use $P=4l$ to solve for $l$ .

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Problem 3319

Shade the area in a Venn diagram representing the set $(A \cap B) \cup (A \cap C)$ .

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Problem 3320

A 336 m street has 4 lamp posts. What is the distance between two consecutive lamp posts?

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Problem 3321

Calculate the cost to lay a concrete patio measuring $10.0 \, \text{ft} \times 60.0 \, \text{ft}$ at \$2.25/m² after converting to meters.

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Problem 3322

Find the volume of a COKE can with base radius $30 \mathrm{~mm}$ and height $130 \mathrm{~mm}$ (in $\mathrm{cm}^{3}$ ).

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Problem 3323

Find the length of side AB in a triangle with sides BC = 2.0m, AC = 5.6m, and angle 20° using the Cosine rule.

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Problem 3324

How many isosceles triangles with whole-number sides have a perimeter of 18? (Hint: 5,5,8 is the smallest.) a. 1 b. 2 c. 3 d. 4

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Problem 3325

Find $\angle B$ in a triangle with $\angle B = 63^{\circ}$ and $\angle C = 63^{\circ}$ . Options: a. $98^{\circ}$ b. $41^{\circ}$ c. $82^{\circ}$ d. $49^{\circ}$ .

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Problem 3326

In a triangle with angles summing to $180^{\circ}$ , if $\angle B = 63^{\circ}$ and $\angle C = 63^{\circ}$ , find $\angle A$ .
Options: a. $m \angle A = 54^{\circ}$ b. $m \angle A = 41^{\circ}$ c. $m \angle A = 82^{\circ}$ d. $m \angle A = 49^{\circ}$

See Solution

Problem 3327

Find angles 1 and 2 in an isosceles triangle. Options: a. $m \angle 1=63^{\circ}, m \angle 2=45^{\circ}$ b. $m \angle 1=45^{\circ}, m \angle 2=63^{\circ}$ c. $m \angle 1=27^{\circ}, m \angle 2=45^{\circ}$ d. $m \angle 1=22.5^{\circ}, m \angle 2=13.5^{\circ}$ .

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Problem 3328

Which angles can form isosceles triangles? Check all that apply. Angles must sum to 180 degrees. a. $24, 24, 50$ b. $32, 32, 116$ c. $79, 79, 22$ d. $21, 53, 106$

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Problem 3329

Which option does NOT describe bisecting: a. Divide into 2 equal parts, b. Split in half, c. Split into 2 congruent pieces, d. Add 2 to all sides/angles?

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Problem 3330

In isosceles triangle $ABC$ , $\angle B=(x+6)^\circ$ and $\angle C=(2x-54)^\circ$ . Given $x=60$ , find the perimeter.

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Problem 3331

In right triangle DOG, with $\angle D = 32^{\circ}$ and $OS$ bisecting $\angle DOG$ , find $\angle OSG$ . Options: a. $58^{\circ}$ b. $77^{\circ}$ c. $103^{\circ}$ d. $122^{\circ}$

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Problem 3332

Find $\angle AMH$ in isosceles triangles $\triangle MAT$ and $\triangle MHT$ with $m \angle MHT=88^{\circ}$ and $m \angle MAT=64^{\circ}$ .

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Problem 3333

Find the length of $TG$ in $\triangle B I G$ where $IG = 7n-3$ and $HA = 3n+1$ . Options: a. 5, b. 3, c. 16, d. 32.

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Problem 3334

Find $T G$ in $\triangle B I G$ where $H, A, T$ are midpoints, $IG = 7n - 3$ , and $HA = 3n + 1$ . Options: a. 5 b. 3 c. 16 d. 32

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Problem 3335

Find the perimeter of parallelogram BUSA, with midpoints $B, U, S$ of triangle sides $CA=5$ , $CR=9$ , $AR=11$ .

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Problem 3336

In triangle $\triangle M A T$ , find $m \angle MAT$ given $m \angle MHA=(6y-6)^{\circ}$ and $m \angle MAT=(3y-7)^{\circ}$ .

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Problem 3337

Find the perimeter of isosceles triangle RST with sides RT = 12.4, RS = 19, and RT = TS. Choices: a. 43.8 b. 62.8 c. 87.6 d. 90

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Problem 3338

Find the perimeter of parallelogram BUSA formed by midpoints B, U, and S of triangle CAR with sides CA=5, CR=9, AR=11.

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Problem 3339

Determine if a triangle with sides 6, 8, and 7 is a right triangle. Choose: A) Yes, B) Yes, C) No, D) No.

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Problem 3340

In a right triangle with sides 5, 8, and 6, label the side measuring 5: A) leg forming right angle B) leg opposite right angle C) hypotenuse forming right angle D) hypotenuse opposite right angle.

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Problem 3341

Is a triangle with angles of 25°, 45°, and 90° a right triangle? Choose the correct option:
(A) Yes, because there is a right angle. (B) Yes, because all sides are equal. (C) No, because there is NO right angle. (D) No, because the sides are not all equal.

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Problem 3342

Label side 'C' in a right triangle with sides 7, 10: A) A leg; it forms the right angle B) A leg; opposite right angle C) Hypotenuse; forms right angle D) Hypotenuse; opposite right angle.

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Problem 3343

Find the length of side C in a right triangle where A = 3 and B = 4 using the formula $C = \sqrt{A^2 + B^2}$ .

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Problem 3344

Simplify $\sqrt{4-x^{2}}$ using the substitution $x=2 \sin \theta$ .

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Problem 3345

In a right triangle with sides 7, 10, and a right angle, what is the label for the side measuring 7?
A) A leg; it forms the right angle B) A leg; it's opposite of the right angle C) Hypotenuse; it forms the right angle D) Hypotenuse; it's opposite of the right angle

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Problem 3346

Find the hypotenuse of a right triangle with sides 12 and 8. Options: A) 12.7 B) 208 C) 14.4 D) 16.5.

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Problem 3347

A COKE can has a radius of 30 mm and height of 130 mm. Find the volume in cm³: $V = \pi r^2 h$ . Then, find the cone's volume with height 3 cm.

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Problem 3348

Find the length of the ladder needed if it reaches 16 feet high and is placed 12 feet from the wall. Use $a^2 + b^2 = c^2$ .

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Problem 3349

Find the length of side $AB$ in a triangle with $BC = 2.0m$ , $AC = 5.6m$ , and an angle of $20$ degrees using the Cosine rule.

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Problem 3350

Find the missing side of a right triangle with sides 3.9 and 11. What is the length? Options: A) 6.5 B) 3.4 C) 11.9 D) 10.3

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Problem 3351

Find side $AB$ of a triangle with sides $a = 2.0m$ , $b = 5.6m$ , and angle $C = 20^\circ$ using the Cosine rule: $c^{2} = a^{2} + b^{2} - 2ab\cos(C)$ .

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Problem 3352

A triangle has a base shorter than its height. Which inequality represents this? A. $3 x-7>2 x+10$ B. $3 x-7 \leq 2 x+10$ C. $2 x+10<3 x-7$

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Problem 3353

In the diagram, $\overrightarrow{X Y}$ bisects $\angle W X Z$ . Given $m \angle W X Y = 7x - 7$ and $m \angle Y X Z = 5x + 3$ , find:
a. $x$ and $m \angle W X Y$ .
b. $m \angle Y X Z$ .
c. $m \angle W X Z$ .

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Problem 3354

In a diagram, line $JG$ is bisected by $KH$ with $\angle HKI = 48^\circ$ . Find the measures of angles HKJ, IKJ, FKG, FKH, FKJ, and GKI.

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Problem 3355

Find the length of $AC$ in triangle ABC if $BC=3$ and $AB=7$ . Possible answers: A) 15 B) 13 C) 10 D) 12

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Problem 3356

Prove that for $\triangle ABC$ with external angle $\angle ACD$ , $m \angle ACD = m \angle B + m \angle A$ .

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Problem 3357

Find the missing mD1 angles when mD3 is 98° and 165° given previous angle sets.

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Problem 3358

Explain why $\overline{B D} \cong \overline{B D}$ in the proof of $\angle A \simeq \angle C$ in $\triangle A B C$ .

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Problem 3359

Sketch the graphs of $f(x)=x^{2}$ and $g(x)=\frac{1}{8} x^{2}$ . Find the points of $g(x)$ corresponding to $(-1,1),(0,0),(1,1)$ .

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Problem 3360

Calculate the distance between points $P(2,8)$ and $Q(5,3)$ . Options: A. 9 B. $\sqrt{18}$ C. $\sqrt{34}$ D. $\sqrt{170}$

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Problem 3361

Calculate the distance between the points $M(-2,3)$ and $N(8,2)$ . Choose from: A. 8 B. $\sqrt{61}$ C. 10 D. $\sqrt{101}$

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Problem 3362

Find point $D(x,y)$ so that line $AB$ is perpendicular to line $CD$ with $A(2,3)$ , $B(8,7)$ , and options for $D$ .

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Problem 3363

A cylinder has a diameter of 10 in and height of 13 in. Find $\theta$ using: A. $\cos (\theta)=\frac{10}{13}$ , B. $\sin (\theta)=\frac{10}{13}$ , C. $\sin (\theta)=\frac{13}{10}$ , D. 10.

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Problem 3364

Quadrilaterals $ABCD$ and $HJKL$ are congruent. Find which angles are congruent: $\angle K \cong$ (A, D, C, or L).

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Problem 3365

Identify the center and radius of these circles and find the standard form for given conditions.
1. $x^{2}+y^{2}=49$
2. $5 x^{2}+5 y^{2}=125$
3. $(x+4)^{2}+(y-2)^{2}=9$
4. center at origin, radius $5 \sqrt{3}$
5. center at $(17,5)$ , radius 12
6. center at $(-8,4)$ , contains $(-4,2)$
7. center at $(15,7)$ , tangent to $x$ -axis.

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Problem 3366

In a figure, $\overline{B G}=\overline{D E}$ . Rectangle $A E F G$ has area 3 times rectangle $A D C B$ . Given width 15 in and length 10 in, find length of $\overline{D E}$ . A. 4 B. 5 C. 6 D. 10

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Problem 3367

Quadrilateral ABCD is congruent to HJKL. Complete: $\overline{J K} \cong$ options: a. $\overline{B C}$ , b. $\overline{C B}$ , c. $\overline{H L}$ , d. $\overline{K J}$ .

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Problem 3368

Pentagon ABCDE is congruent to HJKLP. Complete the congruent statements: $\overline{B A} \cong$ (a) $\overline{H P}$ , (b) $\overline{J P}$ , (c) $\overline{J H}$ , (d) $\overline{J K}$ .

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Problem 3369

Pentagons ABCDE and HJKLP are congruent. Complete: $\overline{C D} \cong$ with options: a) $\overline{L P}$ , b) $\overline{A B}$ , c) $\overline{H J}$ , d) $\overline{K L}$ .

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Problem 3370

Quadrilaterals ABCD and HJKL are congruent. Find $\angle K$ congruent to which angles: A, D, C, or L? Explain your reasoning.

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Problem 3371

Find the distance between VLF transmitters $P$ and $Q$ given $PB = 180$ ft, $PS = 300$ ft, and $QS = 260$ ft. Options: A. 100 B. 230.

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Problem 3372

Find the equation of points equidistant from $(-9,-14)$ and $(-13,2)$ . $y=$

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Problem 3373

What condition makes $\triangle A E D \simeq \triangle C E B$ true? a. $\angle A E D \cong \angle C E B$ b. $\angle E A D \cong \angle E C B$ c. $\angle E D A \cong \angle E B C$ d. $\angle D E C \cong \angle B E A$

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Problem 3374

8. Find the equation for the delivery area around the shop and check if Gericoi qualifies for free delivery.
9. Determine the equation of a circular garden with a diameter of 4 ft, centered 5 ft west and 2 ft south of a cottage.

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Problem 3375

Which statement proves $\triangle D E F \cong \triangle A B C$ ? a. $A B=D E$ , $B C=E F$ b. $\angle D \cong \angle A$ , $\angle B \cong \angle E$ , $\angle C \cong \angle F$ c. Rigid motions map $A$ to $D$ , $A B$ to $D E$ , $\angle B$ to $\angle E$ d. Rigid motions map $A B$ to $D E$ , $B C$ to $E F$ , $A C$ to $D F$ .

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Problem 3376

Find the center and equation of the circle for points $A(-1,-2)$ , $B(6,-9)$ , $C(13,-2)$ , and its diameter in feet.

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Problem 3377

A rectangle's length is 6 times its width. If the perimeter is 70 in, find the area.

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Problem 3378

Find the cost of hardwood floors for a cube room with volume $6,859 \mathrm{ft}^{3}$ at $\$ 10$ per square foot.

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Problem 3379

Yossi's square garage had $282 \mathrm{ft}^{2}$ . After a $50\%$ increase in area, find the original and new side lengths and percent increase.

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Problem 3380

The Bells are adding a cube room with volume $6,859 \mathrm{ft}^{3}$ . Find the cost of hardwood floors at \$10/ft².

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Problem 3381

Which shape must have a square base: cone, pyramid, cube, or rectangular prism?

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Problem 3382

Calculate the volume of a sphere with a diameter of 3 cm. Options: $3 \pi$ , $36 \pi$ , $\frac{9}{2} \pi$ , $\frac{9}{8} \pi$ .

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Problem 3383

Find the distance between a dolphin 18 ft below and a helicopter 75.5 ft above the ocean surface.

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Problem 3384

Find $m \angle RSQ = 15x - 43$ and $m \angle TSQ = 8x + 18$ if they sum to a right angle.

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Problem 3385

Find angles $DEH$ and $FEH$ where $m \angle DEH = 13x$ and $m \angle FEH = 10x + 21$ .

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Problem 3386

Find the angles $m \angle DEH = 13x$ and $m \angle FEH = 10x + 21$ that sum to $90^\circ$ .

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Problem 3387

Find the angles $\angle ABD = 6x + 14$ , $\angle CBD = 3x + 29$ ; determine $\angle ABD$ , $\angle CBD$ , and $\angle ABC$ .

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Problem 3388

Calculate the gallons of water an aquarium (18" wide, 25" long, 12" high) can hold. Use 231 cubic inches/gallon.

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Problem 3389

Find the measures of angles $m \angle A B D$ , $m \angle C B D$ , and $m \angle A B C$ given that $\overrightarrow{B D}$ bisects $\angle A B C$ .

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Problem 3390

In triangle $ABC$ , if $BD$ bisects $\angle ABC$ with $\angle ABC = (2-16x)^\circ$ and $\angle ABD = (2x+81)^\circ$ , find $m \angle ABD$ , $m \angle CBD$ , and $m \angle ABC$ .

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Problem 3391

Find $m \angle A B D$ , $m \angle C B D$ , and $m \angle A B C$ given that $\overrightarrow{B D}$ bisects $\angle A B C$ and $m \angle A B C=(25 x+34)^{\circ}$ .

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Problem 3392

If $BD$ bisects $\angle ABC$ , find $m \angle ABD$ , $m \angle CBD$ , and $m \angle ABC$ with $m \angle ABC = (25x+34)^\circ$ and $m \angle CBD = (11x+22)^\circ$ .

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Problem 3393

Find the measure of angles $\angle A B C$ and $\angle D E F$ , given that $m \angle A B C = 112^{\circ}$ and they are congruent.

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Problem 3394

Find the area, in square inches, of a scale drawing of a classroom floor that is 30 ft by 40 ft with a length of 15 in.

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Problem 3395

Find the perimeter, in inches, of a scale drawing of a classroom floor that is 30 ft long and 24 ft wide, with a 15 in length.

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Problem 3396

Find the area in square inches of a scale drawing of a classroom floor measuring 24 ft by 30 ft, with a length of 4 in.

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Problem 3397

Find the area in square inches of a scale drawing of a classroom floor measuring 24 ft by 40 ft with a length of 6 in.

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Problem 3398

Points A, B, and C are on a line. Find the length $A C$ given $A B$ and $B C$ for two cases.

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Problem 3399

Find $A C$ if points A, B, C, D, and E are in order and $A E=x+50$ , $C E=x+32$ .

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Problem 3400

Create a segment addition problem with points A, B, and C where $AB + BC = AC$ and $x = 20$ .

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Geometry

Problem 3301

Find the angle measures: 3x∘=57∘3x^{\circ}=57^{\circ}3x∘=57∘ and (76−x)∘=(76-x)^{\circ}=(76−x)∘= (Type whole numbers.)

Problem 3302

A rectangular garden is 8 ft longer than its width and has an area of 345 ft². Find its dimensions (width and length).

Problem 3303

Sketch a figure where STundefined\overrightarrow{\mathrm{ST}}ST bisects right ∠PSQ\angle \mathrm{PSQ}∠PSQ. Explain and perform the construction.

Problem 3304

Sketch the figure where STundefined\overrightarrow{S T}ST bisects right ∠PSQ\angle P S Q∠PSQ. What’s the first step? A, B, C, or D?

Problem 3305

Is constructing an angle bisector like constructing a perpendicular bisector? Choose the correct answer below.

Problem 3306

Solve for xxx and find the measures of angles x+11x+11x+11 and 3x−313x-313x−31 given they are congruent.

Problem 3307

Calculate the area of a circle with radius 20 units. Use the formula with π\piπ.

Problem 3308

Construct the bisector of ∠A\angle A∠A. This forms two angles whose measure is 12m∠A\frac{1}{2} m \angle A21​m∠A. Then construct the bisector of one of the resulting angles to form an angle whose measure is 14m∠A\frac{1}{4} m \angle A41​m∠A.

Problem 3309

Divide the line segment PQ‾\overline{P Q}PQ​ into four equal parts using a compass and straightedge. Choose the correct method.

Problem 3310

How to construct a 45∘45^{\circ}45∘ angle? Choose the correct method from the options provided.

Problem 3311

Construct a 45∘45^{\circ}45∘ angle using one of the methods below. Choose A, B, C, or D.

Problem 3312

A triangle with a perimeter of 24 m has equal sides. What is the length of one side?

Problem 3313

Find the length of one side of a square with a perimeter of 12 m12 \mathrm{~m}12 m.

Problem 3314

Graph the equation y=3x−2y=3x-2y=3x−2, find the y-intercept and another point, then draw the line through them.

Problem 3315

Find the missing side length of a figure with a perimeter of 41 cm41 \mathrm{~cm}41 cm, given sides 10 cm10 \mathrm{~cm}10 cm, 14 cm14 \mathrm{~cm}14 cm, and 1 cm1 \mathrm{~cm}1 cm.

Problem 3316

Find the length of one side of a regular pentagon with a perimeter of 20 cm20 \mathrm{~cm}20 cm. What is the length in cm\mathrm{cm}cm?

Problem 3317

A regular pentagon has a perimeter of 20 cm20 \mathrm{~cm}20 cm. Find the length of one side in cm\mathrm{cm}cm.

Problem 3318

Find the missing side of a square with a perimeter of 26 m26 \mathrm{~m}26 m. Use P=4lP=4lP=4l to solve for lll.

Problem 3319

Shade the area in a Venn diagram representing the set (A∩B)∪(A∩C)(A \cap B) \cup (A \cap C)(A∩B)∪(A∩C).

Problem 3320

A 336 m street has 4 lamp posts. What is the distance between two consecutive lamp posts?

Problem 3321

Calculate the cost to lay a concrete patio measuring 10.0 ft×60.0 ft10.0 \, \text{ft} \times 60.0 \, \text{ft}10.0ft×60.0ft at \$2.25/m² after converting to meters.

Problem 3322

Find the volume of a COKE can with base radius 30 mm30 \mathrm{~mm}30 mm and height 130 mm130 \mathrm{~mm}130 mm (in cm3\mathrm{cm}^{3}cm3).

Problem 3323

Find the length of side AB in a triangle with sides BC = 2.0m, AC = 5.6m, and angle 20° using the Cosine rule.

Problem 3324

How many isosceles triangles with whole-number sides have a perimeter of 18? (Hint: 5,5,8 is the smallest.) a. 1 b. 2 c. 3 d. 4

Problem 3325

Find ∠B\angle B∠B in a triangle with ∠B=63∘\angle B = 63^{\circ}∠B=63∘ and ∠C=63∘\angle C = 63^{\circ}∠C=63∘. Options: a. 98∘98^{\circ}98∘ b. 41∘41^{\circ}41∘ c. 82∘82^{\circ}82∘ d. 49∘49^{\circ}49∘.

Problem 3326

Problem 3327

Problem 3328

Which angles can form isosceles triangles? Check all that apply. Angles must sum to 180 degrees. a. 24,24,5024, 24, 5024,24,50 b. 32,32,11632, 32, 11632,32,116 c. 79,79,2279, 79, 2279,79,22 d. 21,53,10621, 53, 10621,53,106

Problem 3329

Which option does NOT describe bisecting: a. Divide into 2 equal parts, b. Split in half, c. Split into 2 congruent pieces, d. Add 2 to all sides/angles?

Problem 3330

In isosceles triangle ABCABCABC, ∠B=(x+6)∘\angle B=(x+6)^\circ∠B=(x+6)∘ and ∠C=(2x−54)∘\angle C=(2x-54)^\circ∠C=(2x−54)∘. Given x=60x=60x=60, find the perimeter.

Problem 3331

In right triangle DOG, with ∠D=32∘\angle D = 32^{\circ}∠D=32∘ and OSOSOS bisecting ∠DOG\angle DOG∠DOG, find ∠OSG\angle OSG∠OSG. Options: a. 58∘58^{\circ}58∘ b. 77∘77^{\circ}77∘ c. 103∘103^{\circ}103∘ d. 122∘122^{\circ}122∘

Problem 3332

Find ∠AMH\angle AMH∠AMH in isosceles triangles △MAT\triangle MAT△MAT and △MHT\triangle MHT△MHT with m∠MHT=88∘m \angle MHT=88^{\circ}m∠MHT=88∘ and m∠MAT=64∘m \angle MAT=64^{\circ}m∠MAT=64∘.

Problem 3333

Find the length of TGTGTG in △BIG\triangle B I G△BIG where IG=7n−3IG = 7n-3IG=7n−3 and HA=3n+1HA = 3n+1HA=3n+1. Options: a. 5, b. 3, c. 16, d. 32.

Problem 3334

Find TGT GTG in △BIG\triangle B I G△BIG where H,A,TH, A, TH,A,T are midpoints, IG=7n−3IG = 7n - 3IG=7n−3, and HA=3n+1HA = 3n + 1HA=3n+1. Options: a. 5 b. 3 c. 16 d. 32

Problem 3335

Find the perimeter of parallelogram BUSA, with midpoints B,U,SB, U, SB,U,S of triangle sides CA=5CA=5CA=5, CR=9CR=9CR=9, AR=11AR=11AR=11.

Problem 3336

In triangle △MAT\triangle M A T△MAT, find m∠MATm \angle MATm∠MAT given m∠MHA=(6y−6)∘m \angle MHA=(6y-6)^{\circ}m∠MHA=(6y−6)∘ and m∠MAT=(3y−7)∘m \angle MAT=(3y-7)^{\circ}m∠MAT=(3y−7)∘.

Problem 3337

Find the perimeter of isosceles triangle RST with sides RT = 12.4, RS = 19, and RT = TS. Choices: a. 43.8 b. 62.8 c. 87.6 d. 90

Problem 3338

Find the perimeter of parallelogram BUSA formed by midpoints B, U, and S of triangle CAR with sides CA=5, CR=9, AR=11.

Problem 3339

Determine if a triangle with sides 6, 8, and 7 is a right triangle. Choose: A) Yes, B) Yes, C) No, D) No.

Problem 3340

In a right triangle with sides 5, 8, and 6, label the side measuring 5: A) leg forming right angle B) leg opposite right angle C) hypotenuse forming right angle D) hypotenuse opposite right angle.

Problem 3341

Find the angle measures: $3x^{\circ}=57^{\circ}$ and $(76-x)^{\circ}=$ (Type whole numbers.)

Sketch a figure where $\overrightarrow{\mathrm{ST}}$ bisects right $\angle \mathrm{PSQ}$ . Explain and perform the construction.

Sketch the figure where $\overrightarrow{S T}$ bisects right $\angle P S Q$ . What’s the first step? A, B, C, or D?

Solve for $x$ and find the measures of angles $x+11$ and $3x-31$ given they are congruent.

Calculate the area of a circle with radius 20 units. Use the formula with $\pi$ .

Construct the bisector of $\angle A$ . This forms two angles whose measure is $\frac{1}{2} m \angle A$ . Then construct the bisector of one of the resulting angles to form an angle whose measure is $\frac{1}{4} m \angle A$ .

Divide the line segment $\overline{P Q}$ into four equal parts using a compass and straightedge. Choose the correct method.

How to construct a $45^{\circ}$ angle? Choose the correct method from the options provided.

Construct a $45^{\circ}$ angle using one of the methods below. Choose A, B, C, or D.

Find the length of one side of a square with a perimeter of $12 \mathrm{~m}$ .

Graph the equation $y=3x-2$ , find the y-intercept and another point, then draw the line through them.

Find the missing side length of a figure with a perimeter of $41 \mathrm{~cm}$ , given sides $10 \mathrm{~cm}$ , $14 \mathrm{~cm}$ , and $1 \mathrm{~cm}$ .

Find the length of one side of a regular pentagon with a perimeter of $20 \mathrm{~cm}$ . What is the length in $\mathrm{cm}$ ?

A regular pentagon has a perimeter of $20 \mathrm{~cm}$ . Find the length of one side in $\mathrm{cm}$ .

Find the missing side of a square with a perimeter of $26 \mathrm{~m}$ . Use $P=4l$ to solve for $l$ .

Shade the area in a Venn diagram representing the set $(A \cap B) \cup (A \cap C)$ .

Calculate the cost to lay a concrete patio measuring $10.0 \, \text{ft} \times 60.0 \, \text{ft}$ at \$2.25/m² after converting to meters.

Find the volume of a COKE can with base radius $30 \mathrm{~mm}$ and height $130 \mathrm{~mm}$ (in $\mathrm{cm}^{3}$ ).

Find $\angle B$ in a triangle with $\angle B = 63^{\circ}$ and $\angle C = 63^{\circ}$ . Options: a. $98^{\circ}$ b. $41^{\circ}$ c. $82^{\circ}$ d. $49^{\circ}$ .

Which angles can form isosceles triangles? Check all that apply. Angles must sum to 180 degrees. a. $24, 24, 50$ b. $32, 32, 116$ c. $79, 79, 22$ d. $21, 53, 106$

In isosceles triangle $ABC$ , $\angle B=(x+6)^\circ$ and $\angle C=(2x-54)^\circ$ . Given $x=60$ , find the perimeter.

In right triangle DOG, with $\angle D = 32^{\circ}$ and $OS$ bisecting $\angle DOG$ , find $\angle OSG$ . Options: a. $58^{\circ}$ b. $77^{\circ}$ c. $103^{\circ}$ d. $122^{\circ}$

Find $\angle AMH$ in isosceles triangles $\triangle MAT$ and $\triangle MHT$ with $m \angle MHT=88^{\circ}$ and $m \angle MAT=64^{\circ}$ .

Find the length of $TG$ in $\triangle B I G$ where $IG = 7n-3$ and $HA = 3n+1$ . Options: a. 5, b. 3, c. 16, d. 32.

Find $T G$ in $\triangle B I G$ where $H, A, T$ are midpoints, $IG = 7n - 3$ , and $HA = 3n + 1$ . Options: a. 5 b. 3 c. 16 d. 32

Find the perimeter of parallelogram BUSA, with midpoints $B, U, S$ of triangle sides $CA=5$ , $CR=9$ , $AR=11$ .

In triangle $\triangle M A T$ , find $m \angle MAT$ given $m \angle MHA=(6y-6)^{\circ}$ and $m \angle MAT=(3y-7)^{\circ}$ .

Is a triangle with angles of 25°, 45°, and 90° a right triangle? Choose the correct option:
(A) Yes, because there is a right angle. (B) Yes, because all sides are equal. (C) No, because there is NO right angle. (D) No, because the sides are not all equal.

Find the length of side C in a right triangle where A = 3 and B = 4 using the formula $C = \sqrt{A^2 + B^2}$ .

Simplify $\sqrt{4-x^{2}}$ using the substitution $x=2 \sin \theta$ .

In a right triangle with sides 7, 10, and a right angle, what is the label for the side measuring 7?
A) A leg; it forms the right angle B) A leg; it's opposite of the right angle C) Hypotenuse; it forms the right angle D) Hypotenuse; it's opposite of the right angle

A COKE can has a radius of 30 mm and height of 130 mm. Find the volume in cm³: $V = \pi r^2 h$ . Then, find the cone's volume with height 3 cm.

Find the length of the ladder needed if it reaches 16 feet high and is placed 12 feet from the wall. Use $a^2 + b^2 = c^2$ .

Find the length of side $AB$ in a triangle with $BC = 2.0m$ , $AC = 5.6m$ , and an angle of $20$ degrees using the Cosine rule.

Find side $AB$ of a triangle with sides $a = 2.0m$ , $b = 5.6m$ , and angle $C = 20^\circ$ using the Cosine rule: $c^{2} = a^{2} + b^{2} - 2ab\cos(C)$ .

A triangle has a base shorter than its height. Which inequality represents this? A. $3 x-7>2 x+10$ B. $3 x-7 \leq 2 x+10$ C. $2 x+10<3 x-7$

In a diagram, line $JG$ is bisected by $KH$ with $\angle HKI = 48^\circ$ . Find the measures of angles HKJ, IKJ, FKG, FKH, FKJ, and GKI.

Find the length of $AC$ in triangle ABC if $BC=3$ and $AB=7$ . Possible answers: A) 15 B) 13 C) 10 D) 12

Prove that for $\triangle ABC$ with external angle $\angle ACD$ , $m \angle ACD = m \angle B + m \angle A$ .

Explain why $\overline{B D} \cong \overline{B D}$ in the proof of $\angle A \simeq \angle C$ in $\triangle A B C$ .

Sketch the graphs of $f(x)=x^{2}$ and $g(x)=\frac{1}{8} x^{2}$ . Find the points of $g(x)$ corresponding to $(-1,1),(0,0),(1,1)$ .

Calculate the distance between points $P(2,8)$ and $Q(5,3)$ . Options: A. 9 B. $\sqrt{18}$ C. $\sqrt{34}$ D. $\sqrt{170}$

Calculate the distance between the points $M(-2,3)$ and $N(8,2)$ . Choose from: A. 8 B. $\sqrt{61}$ C. 10 D. $\sqrt{101}$

Find point $D(x,y)$ so that line $AB$ is perpendicular to line $CD$ with $A(2,3)$ , $B(8,7)$ , and options for $D$ .

A cylinder has a diameter of 10 in and height of 13 in. Find $\theta$ using: A. $\cos (\theta)=\frac{10}{13}$ , B. $\sin (\theta)=\frac{10}{13}$ , C. $\sin (\theta)=\frac{13}{10}$ , D. 10.

Quadrilaterals $ABCD$ and $HJKL$ are congruent. Find which angles are congruent: $\angle K \cong$ (A, D, C, or L).

In a figure, $\overline{B G}=\overline{D E}$ . Rectangle $A E F G$ has area 3 times rectangle $A D C B$ . Given width 15 in and length 10 in, find length of $\overline{D E}$ . A. 4 B. 5 C. 6 D. 10

Quadrilateral ABCD is congruent to HJKL. Complete: $\overline{J K} \cong$ options: a. $\overline{B C}$ , b. $\overline{C B}$ , c. $\overline{H L}$ , d. $\overline{K J}$ .

Pentagon ABCDE is congruent to HJKLP. Complete the congruent statements: $\overline{B A} \cong$ (a) $\overline{H P}$ , (b) $\overline{J P}$ , (c) $\overline{J H}$ , (d) $\overline{J K}$ .

Pentagons ABCDE and HJKLP are congruent. Complete: $\overline{C D} \cong$ with options: a) $\overline{L P}$ , b) $\overline{A B}$ , c) $\overline{H J}$ , d) $\overline{K L}$ .

Quadrilaterals ABCD and HJKL are congruent. Find $\angle K$ congruent to which angles: A, D, C, or L? Explain your reasoning.

Find the distance between VLF transmitters $P$ and $Q$ given $PB = 180$ ft, $PS = 300$ ft, and $QS = 260$ ft. Options: A. 100 B. 230.

Find the equation of points equidistant from $(-9,-14)$ and $(-13,2)$ . $y=$

8. Find the equation for the delivery area around the shop and check if Gericoi qualifies for free delivery.
9. Determine the equation of a circular garden with a diameter of 4 ft, centered 5 ft west and 2 ft south of a cottage.