Question

Janet is designing a frame for a client. She wants to prove to her client that m∠AGE ≅ m∠CHE in her sketch. What is the missing justification in the proof?
Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.


Statement Justification
segment AB is parallel to segment CD with transversal segment EF Given
m∠AGE ≅ m∠HGB Vertical Angles Theorem
m∠HGB ≅ m∠CHE Alternate Interior Angles Theorem
m∠AGE ≅ m∠CHE
Alternate Exterior Angles Theorem
Corresponding Angles Theorem
Reflexive Property
Transitive Property

Answer 1

The missing justification for m∠AGE ≅ m∠CHE is: B. Corresponding Angles Theorem.

When two parallel lines are cut across by a transversal line, two angles formed that are in the same position along the intersected lines are corresponding angles.

According to the corresponding angles theorem, corresponding angles formed when two parallel lines are cut across by a transversal are congruent to each other.

In the diagram given, ∠AGE and ∠CHE are corresponding angles. The two angles are congruent.

Therefore, the missing justification for the statement, m∠AGE ≅ m∠CHE, is Corresponding Angles Theorem.

Learn more about about corresponding angles theorem here:

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