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

To prove that Triangle A B C is congruent to Triangle F G H using the provided information, we can analyze each step based on the given conditions.

1. **Step 1**: We know that Angle A B C is congruent to Angle F G H because all right angles are congruent. (This is true since both angles are right angles.)

2. **Step 2**: We know that Angle B A C is congruent to Angle G F H because corresponding angles of parallel lines are congruent. (This is also true because lines BA and GF are parallel and BC is a transversal line.)

3. **Step 3**: We know that Line segment B C is congruent to Line segment G H because it is given.

Now, we have established the following:

- Angle A B C ≅ Angle F G H (both are right angles)
- Angle B A C ≅ Angle G F H (corresponding angles)
- Line segment B C ≅ Line segment G H (given)

4. **Conclusion**: Triangle A B C is congruent to Triangle F G H by the **Angle-Side-Angle (ASA) congruence theorem**. This is because we have two angles and the included side of one triangle that are congruent to the two angles and the included side of the other triangle.

Thus, the best choice to complete the proof is:

**ASA congruence theorem.**