Question

Given: Angle A B C and Angle F G H are right angles; Line segment B A is parallel to line segment G F; Line segment B C is-congruent-to line segment G H
Prove: Triangle A B C Is-congruent-to Triangle F G H

Triangles A B C and F G H are shown. Triangle F G H is slightly lower and to the left of triangle A B C. Lines extend from sides B A and G F to form parallel lines. Another line connects points F and C. Angles A B C and F G H are right angles. Sides B C and G H are congruent.

Step 1: We know that Angle A B C Is-congruent-to Angle F G H because all right angles are congruent.
Step 2: We know that Angle B A C Is-congruent-to Angle G F H because corresponding angles of parallel lines are congruent.
Step 3: We know that Line segment B C is-congruent-to line segment G H because it is given.
Step 4: Triangle A B C Is-congruent-to Triangle F G H because of the

ASA congruence theorem.
AAS congruence theorem.
third angle theorem.
reflexive property.

Answer 1

AAS congruence theorem.

Reason: From Steps 1 and 2 we have two pairs of corresponding angles congruent (∠ABC ≅ ∠FGH and ∠BAC ≅ ∠GFH). Step 3 gives the pair of corresponding non‑included sides BC ≅ GH (BC is opposite ∠A, GH is opposite ∠F). Two angles and a non‑included corresponding side imply triangle congruence by AAS, so △ABC ≅ △FGH.