The two angles ∠AGF and ∠EHD are congruent.
What is congruency?
The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one are congruent to the included angle and corresponding two sides of the other triangle.
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. ∠AGF and ∠EGB are vertical and congruent by the Vertical Angles Theorem.
∠EGB and ∠EHD are congruent according to the Corresponding Angles Theorem; Finally, ∠AGF and ∠EHD are congruent by the Transitive Property of Equality.
Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠EGB and ∠EHD are congruent
Corresponding Angles Theorem; ∠EGB and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠AGF and ∠EHD are congruent
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