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

The missing statements are,

In first blank:  ∠2≅∠1

In second blank:  AC≅AC

In third blank:  Reflexive

Step-by-step explanation:

Since, The hypotenuse angle theorem states that if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent to each other.

Here, given:

∠D and ∠B are right angles.

DC ║ AB

Prove: Δ ADC ≅ Δ CBA

              Statement                                       Reason

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

2. ∠2 ≅ ∠1                                      2. If lines are parallel then interior angles

                                                        are equal

3. AC≅AC                                      3. Reflexive

4.Δ ADC ≅ Δ CBA                        4. Hypotenuse angle theorem

step-by-step explanation:

given: ∠d and ∠b are right angles dc || ab.

to prove: △adc ≅ △cba

proof:

statement                                                                   reason

1. ∠d and ∠b are right angles                                 given

2. ac=ac                                                               common hypotenuse

3. △adc ≅ △cba                                                 hypotenuse angle theorem

therefore, △adc ≅ △cba by hl theorem.

hence proved.

Step-by-step explanation:

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