Math / Geometry

QuestionGiven that lines $m$ and $n$ are parallel and cut by transversal $t$ , which pair of angles are NOT congruent? $\angle 1$ and $\angle 5$ $\angle 2$ and $\angle 6$ $\angle 3$ and $\angle 5$ $\angle 1$ and $\angle 6$

Studdy Solution

STEP 1

What is this asking? Which angles, when two parallel lines are crossed by another line, aren't the same size? Watch out! Don't mix up corresponding and alternate angles!

STEP 2

1. Corresponding Angles
2. Alternate Interior Angles
3. The Odd One Out

STEP 3

When a line crosses two parallel lines, some angles are equal!
These are called corresponding angles.
They're in matching positions on each parallel line.

STEP 4

Look at $\angle 1$ and $\angle 5$ .
See how they're both above the parallel lines and on the same side of the crossing line?
That makes them corresponding angles, so $\angle 1 = \angle 5$ .

STEP 5

Similarly, $\angle 2$ and $\angle 6$ are corresponding angles.
They're both above the parallel lines and on the same side of the crossing line.
So, $\angle 2 = \angle 6$ .

STEP 6

Alternate interior angles are also equal!
They're inside the parallel lines, but on opposite sides of the crossing line.

STEP 7

$\angle 3$ and $\angle 5$ are alternate interior angles. $\angle 3$ is below line $m$ and to the right of line $t$ , while $\angle 5$ is above line $n$ and to the left of line $t$ .
Since they're alternate interior angles, $\angle 3 = \angle 5$ .

STEP 8

We've seen that $\angle 1 = \angle 5$ , $\angle 2 = \angle 6$ , and $\angle 3 = \angle 5$ .
What about $\angle 1$ and $\angle 6$ ?

STEP 9

$\angle 1$ is above line $m$ and to the left of line $t$ , while $\angle 6$ is above line $n$ and to the right of line $t$ .
They're not corresponding angles, and they're not alternate interior angles.

STEP 10

In fact, $\angle 1$ and $\angle 2$ add up to $180^\circ$ because they're adjacent angles on a straight line.
Since $\angle 2 = \angle 6$ , we know that $\angle 1$ and $\angle 6$ can't be equal!

STEP 11

$\angle 1$ and $\angle 6$ are not congruent.

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QuestionGiven that lines $m$ and $n$ are parallel and cut by transversal $t$ , which pair of angles are NOT congruent? $\angle 1$ and $\angle 5$ $\angle 2$ and $\angle 6$ $\angle 3$ and $\angle 5$ $\angle 1$ and $\angle 6$

Studdy Solution

STEP 1

What is this asking? Which angles, when two parallel lines are crossed by another line, aren't the same size? Watch out! Don't mix up corresponding and alternate angles!

STEP 2

1. Corresponding Angles
2. Alternate Interior Angles
3. The Odd One Out

STEP 3

When a line crosses two parallel lines, some angles are equal!
These are called corresponding angles.
They're in matching positions on each parallel line.

STEP 4

Look at $\angle 1$ and $\angle 5$ .
See how they're both above the parallel lines and on the same side of the crossing line?
That makes them corresponding angles, so $\angle 1 = \angle 5$ .

STEP 5

Similarly, $\angle 2$ and $\angle 6$ are corresponding angles.
They're both above the parallel lines and on the same side of the crossing line.
So, $\angle 2 = \angle 6$ .

STEP 6

Alternate interior angles are also equal!
They're inside the parallel lines, but on opposite sides of the crossing line.

STEP 7

$\angle 3$ and $\angle 5$ are alternate interior angles. $\angle 3$ is below line $m$ and to the right of line $t$ , while $\angle 5$ is above line $n$ and to the left of line $t$ .
Since they're alternate interior angles, $\angle 3 = \angle 5$ .

STEP 8

We've seen that $\angle 1 = \angle 5$ , $\angle 2 = \angle 6$ , and $\angle 3 = \angle 5$ .
What about $\angle 1$ and $\angle 6$ ?

STEP 9

$\angle 1$ is above line $m$ and to the left of line $t$ , while $\angle 6$ is above line $n$ and to the right of line $t$ .
They're not corresponding angles, and they're not alternate interior angles.

STEP 10

In fact, $\angle 1$ and $\angle 2$ add up to $180^\circ$ because they're adjacent angles on a straight line.
Since $\angle 2 = \angle 6$ , we know that $\angle 1$ and $\angle 6$ can't be equal!

STEP 11

$\angle 1$ and $\angle 6$ are not congruent.

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QuestionGiven that lines mmm and nnn are parallel and cut by transversal ttt, which pair of angles are NOT congruent? ∠1\angle 1∠1 and ∠5\angle 5∠5 ∠2\angle 2∠2 and ∠6\angle 6∠6 ∠3\angle 3∠3 and ∠5\angle 5∠5 ∠1\angle 1∠1 and ∠6\angle 6∠6

Studdy Solution

STEP 1

What is this asking? Which angles, when two parallel lines are crossed by another line, *aren't* the same size? Watch out! Don't mix up corresponding and alternate angles!

STEP 2

1. Corresponding Angles2. Alternate Interior Angles3. The Odd One Out

STEP 3

When a line crosses two parallel lines, some angles are **equal**!These are called **corresponding angles**.They're in matching positions on each parallel line.

STEP 4

Look at ∠1\angle 1∠1 and ∠5\angle 5∠5.See how they're both above the parallel lines and on the same side of the crossing line?That makes them **corresponding angles**, so ∠1=∠5\angle 1 = \angle 5∠1=∠5.

STEP 5

Similarly, ∠2\angle 2∠2 and ∠6\angle 6∠6 are corresponding angles.They're both above the parallel lines and on the same side of the crossing line.So, ∠2=∠6\angle 2 = \angle 6∠2=∠6.

STEP 6

**Alternate interior angles** are also **equal**!They're inside the parallel lines, but on opposite sides of the crossing line.

STEP 7

∠3\angle 3∠3 and ∠5\angle 5∠5 are alternate interior angles. ∠3\angle 3∠3 is below line mmm and to the right of line ttt, while ∠5\angle 5∠5 is above line nnn and to the left of line ttt.Since they're alternate interior angles, ∠3=∠5\angle 3 = \angle 5∠3=∠5.

STEP 8

We've seen that ∠1=∠5\angle 1 = \angle 5∠1=∠5, ∠2=∠6\angle 2 = \angle 6∠2=∠6, and ∠3=∠5\angle 3 = \angle 5∠3=∠5.What about ∠1\angle 1∠1 and ∠6\angle 6∠6?

STEP 9

∠1\angle 1∠1 is above line mmm and to the left of line ttt, while ∠6\angle 6∠6 is above line nnn and to the right of line ttt.They're not corresponding angles, and they're not alternate interior angles.

STEP 10

In fact, ∠1\angle 1∠1 and ∠2\angle 2∠2 add up to 180∘180^\circ180∘ because they're adjacent angles on a straight line.Since ∠2=∠6\angle 2 = \angle 6∠2=∠6, we know that ∠1\angle 1∠1 and ∠6\angle 6∠6 *can't* be equal!

STEP 11

∠1\angle 1∠1 and ∠6\angle 6∠6 are not congruent.

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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.

QuestionGiven that lines $m$ and $n$ are parallel and cut by transversal $t$ , which pair of angles are NOT congruent? $\angle 1$ and $\angle 5$ $\angle 2$ and $\angle 6$ $\angle 3$ and $\angle 5$ $\angle 1$ and $\angle 6$

What is this asking? Which angles, when two parallel lines are crossed by another line, aren't the same size? Watch out! Don't mix up corresponding and alternate angles!

1. Corresponding Angles
2. Alternate Interior Angles
3. The Odd One Out

When a line crosses two parallel lines, some angles are equal!
These are called corresponding angles.
They're in matching positions on each parallel line.

Look at $\angle 1$ and $\angle 5$ .
See how they're both above the parallel lines and on the same side of the crossing line?
That makes them corresponding angles, so $\angle 1 = \angle 5$ .

Similarly, $\angle 2$ and $\angle 6$ are corresponding angles.
They're both above the parallel lines and on the same side of the crossing line.
So, $\angle 2 = \angle 6$ .

Alternate interior angles are also equal!
They're inside the parallel lines, but on opposite sides of the crossing line.

$\angle 3$ and $\angle 5$ are alternate interior angles. $\angle 3$ is below line $m$ and to the right of line $t$ , while $\angle 5$ is above line $n$ and to the left of line $t$ .
Since they're alternate interior angles, $\angle 3 = \angle 5$ .

We've seen that $\angle 1 = \angle 5$ , $\angle 2 = \angle 6$ , and $\angle 3 = \angle 5$ .
What about $\angle 1$ and $\angle 6$ ?

$\angle 1$ is above line $m$ and to the left of line $t$ , while $\angle 6$ is above line $n$ and to the right of line $t$ .
They're not corresponding angles, and they're not alternate interior angles.

In fact, $\angle 1$ and $\angle 2$ add up to $180^\circ$ because they're adjacent angles on a straight line.
Since $\angle 2 = \angle 6$ , we know that $\angle 1$ and $\angle 6$ can't be equal!

$\angle 1$ and $\angle 6$ are not congruent.