Question

In the proof of the alternate exterior angles theorem, segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H. It is given that segment AB is parallel to segment CD and points E, G, H, and F are collinear. ________ by the vertical angles theorem. a) ∠EGA and ∠AGF are congruent; transitive property of equality b) ∠EGA and ∠AGF are congruent; subtraction property c) ∠EGB and ∠AGF are congruent; transitive property of equality d) ∠EGB and ∠EGA are congruent; subtraction property

Answer 1

The correct answer is option (c) ∠EGB and ∠AGF are congruent; transitive property of equality.

Step-by-step explanation:

The correct answer is option (c) ∠EGB and ∠AGF are congruent; transitive property of equality.

According to the Vertical Angles Theorem, when two lines intersect, the pairs of vertical angles are congruent. In this case, ∠EGB and ∠AGF are vertical angles formed by the intersecting transversal EF and parallel lines AB and CD. Therefore, ∠EGB and ∠AGF are congruent.

Option (d), ∠EGB and ∠EGA are congruent; subtraction property, is incorrect because the subtraction property does not apply to the given scenario.

Learn more about Alternate Exterior Angles Theorem