Math / Geometry

QuestionListen
Decide whether there is enough information to prove that $\triangle W X Z \simeq \triangle Y Z X$ using the SAS Congruence Theorem. Explain your reasoning, yes; Because $\overline{Z W} \simeq \overline{X Y}, \angle W \simeq \angle Y$ , and $\overline{W X} \simeq \overline{Y Z}$ , the two triangles are congruent by the SAS Congruence Theorem. yes; Because $\overline{Z W} \simeq \overline{X Y}, \angle W \simeq \angle Y$ , and $\overline{Z X} \simeq \overline{X Z}$ , the two triangles are congruent by the SAS Congruence Theorem. no; There is one pair of congruent sides and one pair of congruent angles, but there is no other pair of congruent sides. no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.

Studdy Solution

STEP 1

What is this asking? Do we have enough info to say that triangle WXZ and triangle YZX are the same using the Side-Angle-Side rule? Watch out! The SAS rule needs two matching sides and the angle between them to be the same.

STEP 2

1. Check what we know.
2. See if it fits the SAS rule.

STEP 3

Alright, so we're looking at triangles WXZ and YZX.
Let's see what's the same in both.
We know that $\overline{ZW}$ and $\overline{XY}$ are congruent.
Awesome! That's one pair of sides.
We also know that angles $\angle W$ and $\angle Y$ are congruent.
Great! That's a pair of angles.

STEP 4

Now, we need another pair of sides.
We know that $\overline{ZX}$ is a shared side, which means it's the same in both triangles!
So, $\overline{ZX}$ is congruent to itself, or $\overline{ZX} \simeq \overline{XZ}$ .
That's our second pair of sides!

STEP 5

Remember, for SAS, the angle has to be between the two sides.
Let's look at triangle WXZ.
We have sides $\overline{ZW}$ and $\overline{ZX}$ , and the angle between them is $\angle Z$ .

STEP 6

Now, triangle YZX.
We have sides $\overline{XY}$ and $\overline{ZX}$ , and the angle between them is $\angle X$ .

STEP 7

We know that $\angle W \simeq \angle Y$ , but we don't know if $\angle Z \simeq \angle X$ .
Since we don't have the angle between the two matching sides, we can't use SAS.

STEP 8

The answer is no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.

Was this helpful?

Studdy Solution

STEP 1

What is this asking? Do we have enough info to say that triangle WXZ and triangle YZX are the same using the Side-Angle-Side rule? Watch out! The SAS rule needs two matching sides and the angle between them to be the same.

STEP 2

1. Check what we know.
2. See if it fits the SAS rule.

STEP 3

Alright, so we're looking at triangles WXZ and YZX.
Let's see what's the same in both.
We know that $\overline{ZW}$ and $\overline{XY}$ are congruent.
Awesome! That's one pair of sides.
We also know that angles $\angle W$ and $\angle Y$ are congruent.
Great! That's a pair of angles.

STEP 4

Now, we need another pair of sides.
We know that $\overline{ZX}$ is a shared side, which means it's the same in both triangles!
So, $\overline{ZX}$ is congruent to itself, or $\overline{ZX} \simeq \overline{XZ}$ .
That's our second pair of sides!

STEP 5

Remember, for SAS, the angle has to be between the two sides.
Let's look at triangle WXZ.
We have sides $\overline{ZW}$ and $\overline{ZX}$ , and the angle between them is $\angle Z$ .

STEP 6

Now, triangle YZX.
We have sides $\overline{XY}$ and $\overline{ZX}$ , and the angle between them is $\angle X$ .

STEP 7

We know that $\angle W \simeq \angle Y$ , but we don't know if $\angle Z \simeq \angle X$ .
Since we don't have the angle between the two matching sides, we can't use SAS.

STEP 8

The answer is no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? Do we have enough info to say that triangle WXZ and triangle YZX are the same using the Side-Angle-Side rule? Watch out! The SAS rule needs two matching sides and the angle *between* them to be the same.

STEP 2

1. Check what we know.2. See if it fits the SAS rule.

STEP 3

STEP 4

Now, we need another pair of sides.We know that ZX‾\overline{ZX}ZX is a shared side, which means it's the same in both triangles!So, ZX‾\overline{ZX}ZX is congruent to itself, or ZX‾≃XZ‾\overline{ZX} \simeq \overline{XZ}ZX≃XZ.That's our second pair of sides!

STEP 5

Remember, for SAS, the angle has to be *between* the two sides.Let's look at triangle WXZ.We have sides ZW‾\overline{ZW}ZW and ZX‾\overline{ZX}ZX, and the angle between them is ∠Z\angle Z∠Z.

STEP 6

Now, triangle YZX.We have sides XY‾\overline{XY}XY and ZX‾\overline{ZX}ZX, and the angle between them is ∠X\angle X∠X.

STEP 7

We know that ∠W≃∠Y\angle W \simeq \angle Y∠W≃∠Y, but we *don't* know if ∠Z≃∠X\angle Z \simeq \angle X∠Z≃∠X.Since we don't have the angle *between* the two matching sides, we can't use SAS.

STEP 8

The answer is no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Do we have enough info to say that triangle WXZ and triangle YZX are the same using the Side-Angle-Side rule? Watch out! The SAS rule needs two matching sides and the angle between them to be the same.

1. Check what we know.
2. See if it fits the SAS rule.

Now, we need another pair of sides.
We know that $\overline{ZX}$ is a shared side, which means it's the same in both triangles!
So, $\overline{ZX}$ is congruent to itself, or $\overline{ZX} \simeq \overline{XZ}$ .
That's our second pair of sides!

Remember, for SAS, the angle has to be between the two sides.
Let's look at triangle WXZ.
We have sides $\overline{ZW}$ and $\overline{ZX}$ , and the angle between them is $\angle Z$ .

Now, triangle YZX.
We have sides $\overline{XY}$ and $\overline{ZX}$ , and the angle between them is $\angle X$ .

We know that $\angle W \simeq \angle Y$ , but we don't know if $\angle Z \simeq \angle X$ .
Since we don't have the angle between the two matching sides, we can't use SAS.