Question

the proof that △abc≅△dcb is shown. given: ∠a≅∠d; cd∥ab prove: △abc≅△dcb
statement reason

1. ∠a≅∠d 1. given
2. cd∥ab 2. given
3. cb≅bc 3. refl. prop.
4. ∠abc≅∠dcb 4. alt. int. ∠s are ≅
5. △abc≅△dcb 5.? what is the missing reason in the proof? asa aas alt. ext. ∠s are ≅ corr. int. ∠s are ≅

Explanation:

Step1: Recall triangle - congruence postulates

We have two angles and a non - included side.

Step2: Identify the postulate

We know that $\angle A\cong\angle D$ (given), $\angle ABC\cong\angle DCB$ (alternate interior angles are congruent), and $\overline{CB}\cong\overline{BC}$ (reflexive property). This is the Angle - Angle - Side (AAS) congruence postulate.

Answer:

AAS