Prove: ∠JNM ≅ ∠NMI

According to the given information in the image, segment JK is parallel to segment HI while ∠JNM and ∠LNK are vertical angles. ∠JNM and ∠LNK are congruent by the Vertical Angles Theorem. Because ∠LNK and ∠NMI are corresponding angles, they are congruent according to the Corresponding Angles Theorem. Finally, ∠JNM is congruent to ∠NMI by the Transitive Property of Equality.

Alternate Interior Angles Theorem
Corresponding Angles Theorem
Vertical Angles Theorem
Same-Side Interior Angles Theorem

To put it simply; they are both internal angles. N is the internal line and as both JNM and NMI are angles that use the line N both are interior angles. They are clearly on oppisite sides of the line N, making them "Alternate Interior Angles".

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-07-13T11:06:35+02:00

The answer is the Alternate Interior Angles Theorem option first is correct.

What are vertically opposite angles?

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

The missing figure is attached in the picture please refer to the picture.

We have:

Segment JK is parallel to segment HI while ∠JNM and ∠LNK are vertical angles. ∠JNM and ∠LNK are congruent by the Vertical Angles Theorem

As we know, both angles have internal angles. Since JNM and NMI are angles that both employ the internal line N, they are both interior angles. N is the internal line.

Thus, the answer is the Alternate Interior Angles Theorem option first is correct.

Learn more about the vertically opposite angles here:

brainly.com/question/24287162

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