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: Identify known congruent parts

We have $\angle A\cong\angle D$ (given), $\angle ABC\cong\angle DCB$ (alternate - interior angles are congruent as $CD\parallel AB$) and $CB\cong BC$ (reflexive property).

Step2: Recall triangle - congruence postulates

The Angle - Angle - Side (AAS) 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. Here, the non - included side is $CB$ for both $\triangle ABC$ and $\triangle DCB$.

Answer:

AAS