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

Answer 1

The Hypotenuse Angle Theorem states that if one acute angle and the hypotenuse of the two right angled triangles are congruent then the triangles are congruent.

ADC is congruent to triangle CBA given that ∠D and ∠B are right angles and DC is parallel to AB.

 

Given: ∠D and ∠B are right angles

DC || AB  

Prove: △ADC ≅ △CBA  

 

 

STATEMENT                                      REASON

1.∠D and ∠B are right angles         1. Given  

2.  ∠1=∠ 2                                          2. If lines are parallel, then alternate                

                                                              Interior angles are equal

3.  AC ≅ AC                                      3. Common to both △s

4.  △ADC ≅ △CBA                           4. Hypotenuse Angle Theorem

     

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