Question

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

The correct congruence theorem for Step 4 is the AAS Congruence Theorem.

How to prove the given angles

Given: Angle ABC and Angle FGH are right angles; Line segment BA is parallel to line segment GF; Line segment BC is congruent to line segment GH.

Step 1: We know that Angle ABC is congruent to Angle FGH because all right angles are congruent.

Step 2: We know that Angle BAC is congruent to Angle GFH because corresponding angles of parallel lines are congruent.

Step 3: We know that Line segment BC is congruent to line segment GH because it is given.

Step 4: Triangle ABC is congruent to Triangle FGH because of the Angle-Angle-Side (AAS) congruence theorem. This is because we have established the following congruence conditions: Angle BAC ≅ Angle GFH (Angle), Angle ABC ≅ Angle FGH (Angle), and BC ≅ GH (Side).

Therefore, the correct congruence theorem for Step 4 is the AAS Congruence Theorem.