Question

the proof △abc≅△dcb that is shown. given: ∠a≅∠d; cd||ab prove: △abc≅△dcb what is the missing reason in the proof? 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? alt. ext. ∠s are ≅ asa aas corr. int. ∠s are ≅

Explanation:

Step1: Recall triangle - congruence postulates

We know the following triangle - congruence postulates: ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), SSS (Side - Side - Side), SAS (Side - Angle - Side).

Step2: Identify the given congruent parts

We are given that $\angle A\cong\angle D$, $\angle ABC\cong\angle DCB$, and $\overline{CB}\cong\overline{BC}$.

Step3: Determine the congruence postulate

We have two pairs of angles and a non - included side congruent. The AAS (Angle - Angle - Side) postulate states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

AAS