Question

PLEASE HELP!!

Answer 1

Answer:

A because when two angles appear in the same orientation, like EGB and EHD, they are corresponding, and thus congruent. When 2 things are equal to the same thing, like AGF and EHD being congruent to EGB, we can call the two congruent using the transitive property of congruence.

Answer 2

Answer:  Choice A

Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent

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Explanation:

∠EGB and ∠EHD are angles that are both on the right hand side of the transversal line EF. Also, these two angles are above their adjacent parallel line. In other words, ∠EGB is above line AB, while ∠EHD is above line CD.

So this all means ∠EGB and ∠EHD are corresponding angles. By the corresponding angles theorem, we can go from AB and CD being parallel to ∠EGB = ∠EHD.

Earlier it was shown that ∠AGF = ∠EGB. Combine this with ∠EGB = ∠EHD, and we can effectively chain the statements together to end up with ∠AGF = ∠EHD.

In terms of a math term, we used the transitive property of equality. This property says that if a = b and b = c, then a = c. You can think of three towns A, B, C. If you go from town A to town B, then town B to town C, then overall you went from town A to town C. We can write it as such $A \to B, \ \text{ and } \ B \to C$ which simplifies to $A \to C$