Give the missing reasons in this proof of the alternate interior angles theorem

Asked by maham237 @ in Mathematics viewed by 300 People

Can someone please help me with this problem?
Give the missing reasons in this proof of the Alternate Interior Angles Theorem.

Given: L is parallel to n.
Prove: angle 4 ≅ angle 6

1. L is parallel to n 1. Given
2. angle 2 ≅ angle 6 a. ???
3. angle 4 ≅ angle 2 b. ???
4. angle 6 ≅ angle 4 c. ???

Answered by maham237 @


1. L is parallel to n 1. Given
2. angle 2 ≅ angle 6 a. corresponding angles
3. angle 4 ≅ angle 2 b. vertical angles
4. angle 6 ≅ angle 4 c. alternate interior angles

corresponding angles are angles found in matching corners.
vertical angles are angles that share the same vertex
alternate interior angles are angles found on the opposite sides of the transversal but inside the two parallel lines

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