Question

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that triangle ADC is congruent to triangle CBA given that ∠D and ∠B are right angles and DC is parallel to AB. Upload the entire proof below.

Given:
∠D and ∠B are right angles
DC || AB

Prove:
△ADC ≅ △CBA


STATEMENT REASON
1.∠D and ∠B are right angles

DC || AB

1. Given
2. 2. If lines are parallel, then alternate interior angles are equal
3. 3.
4. 4. Hypotenuse Angle Theorem

Answer 1

To prove that triangle ADC is congruent to triangle CBA, we can use the Angle-Angle (AA) similarity theorem. First, we use the fact that ∠D and ∠B are right angles and DC is parallel to AB to show that corresponding angles are congruent. Then, we conclude that triangle ADC and triangle CBA have two pairs of congruent angles, which implies congruency.

Step-by-step explanation:

To prove that triangle ADC is congruent to triangle CBA, we will use a two-column proof.

1. Given: ∠D and ∠B are right angles, DC || AB
2. Parallel lines have congruent alternate interior angles
3. Therefore, ∠DAC = ∠CBA (corresponding angles)
4. For the same reason, ∠CDA = ∠ACB
5. Triangle ADC and triangle CBA have two pairs of congruent angles
6. Therefore, by the Angle-Angle (AA) similarity theorem, triangle ADC is congruent to triangle CBA