Question

1. given: ( overline{ab} cong overline{ed} ), ( overline{ad} cong overline{eb} ) prove: ( \triangle abd cong \triangle edb ) look at the proof. name the postulate you would use to prove the two triangles are congruent. given: ( overline{ab} cong overline{ed}, overline{ad} cong overline{eb} ) prove: ( \triangle abd cong \triangle edb ) ( overline{ab} cong overline{ed} ) given ( overline{ad} cong overline{eb} ) given ( overline{bd} cong overline{bd} ) reflexive property of congruence ( \triangle abd cong \triangle edb )? sss postulate sas postulate aaa postulate

Explanation:

Step1: Recall triangle congruence postulates

SSS (Side - Side - Side) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. SAS (Side - Angle - Side) postulate requires two sides and the included angle to be congruent. AAA (Angle - Angle - Angle) does not prove triangle congruence (it proves similarity).

Step2: Analyze the given congruent sides

We are given \(AB\cong ED\), \(AD\cong EB\), and \(BD\cong BD\) (reflexive property). So, we have three pairs of congruent sides.

Answer:

SSS Postulate