Math  /  Geometry

QuestionLLundefined\overleftrightarrow{L L} and MOundefined\overleftrightarrow{M O} are parallel lines.
Which angles are alternate interior angles? JKN\angle J K N and ONP\angle O N P

Studdy Solution

STEP 1

What is this asking? Which angles are *between* the parallel lines and on *opposite* sides of the line that crosses them? Watch out! Don't mix up alternate interior angles with other types of angles, like corresponding or alternate exterior angles!

STEP 2

1. Locate the parallel lines and the transversal.
2. Identify the interior angles.
3. Find the alternate interior angle pairs.

STEP 3

Alright, so we've got our parallel lines JLundefined\overleftrightarrow{JL} and MOundefined\overleftrightarrow{MO}, and they're crossed by another line, NPundefined\overleftrightarrow{NP}, which we call a **transversal**!

STEP 4

The **interior angles** are the angles *between* the parallel lines.
Imagine the parallel lines are the walls of a hallway.
The angles inside that hallway are our interior angles.
In our case, those are JKN\angle JKN, LKN\angle LKN, MNP\angle MNP, and ONP\angle ONP.

STEP 5

**Alternate interior angles** are interior angles that are on *opposite* sides of the transversal.
Think of it like this: if you're walking down the hallway (the transversal), alternate interior angles would be on opposite sides of you.

STEP 6

Let's look at our options. JKN\angle JKN is on one side of the transversal, and ONP\angle ONP is on the other side.
Both are interior angles.
So, JKN\angle JKN and ONP\angle ONP are **alternate interior angles**!

STEP 7

The other pair of alternate interior angles would be LKN\angle LKN and MNP\angle MNP.

STEP 8

The alternate interior angles are JKN\angle JKN and ONP\angle ONP, and also LKN\angle LKN and MNP\angle MNP.

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