Question

Julia is designing a frame for a client. She wants to prove to her client that m∠AGE ≅ m∠FHD 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∠FHD
∠AGE ≅ ∠FHD Transitive Property
Group of answer choices

Alternate Exterior Angles Theorem

Corresponding Angles Theorem

Reflexive Property

Substitution Property​

Answer 1

The missing justification in Julia's angle proof is; Corresponding Angles Theorem

What is the angle theorem used?

We know that m∠AGE ≅ m∠HGB because they have congruent angles and are vertical angles.

Similarly, m∠HGB ≅ m∠CHE are alternate interior angles because two congruent angles on the inner side of the parallel lines are formed by a transversal.

In the diagram, m∠AGE ≅ m∠CHE would have to be corresponding Angles Theorem because parallel lines cut by a transversal would create congruent corresponding angles. That means a pair of angles on the same side of one of two lines that is cut by a transversal and on the same side of the transversal.

Read more about Angle theorem at; brainly.com/question/24839702

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