Question

triangle proofs
no late credit
grade: 0%
complete: 59%
interior and exterior triangle angles
triangle congruence criteria
triangle congruence, basic flowchart proof
triangle congruence, flowchart proof (level 1)
answer attempt 1 out of 2
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scientific calculator
graphing calculator
∠bdc≅∠bea
reason:
select reason
cd≅ae
reason:
select reason
∠b≅∠b
reason:
select reason
△abe≅△cbd
reason:
select reason

Explanation:

Step1: Identify angle - angle - side (AAS) criterion

We have one pair of congruent angles ($\angle BDC\cong\angle BEA$), one pair of congruent non - included sides ($\overline{CD}\cong\overline{AE}$), and a common angle ($\angle B\cong\angle B$).

Step2: Determine congruence reason for $\angle BDC\cong\angle BEA$

If not given as a given statement in the problem, we would need more context. But if it is given information, the reason is "Given".

Step3: Determine congruence reason for $\overline{CD}\cong\overline{AE}$

If it is given information in the problem, the reason is "Given".

Step4: Determine congruence reason for $\angle B\cong\angle B$

This is the reflexive property of congruence which states that any angle is congruent to itself.

Step5: Determine congruence reason for $\triangle ABE\cong\triangle CBD$

Since we have two angles and a non - included side of one triangle congruent to two angles and the corresponding non - included side of another triangle, the reason is "AAS (Angle - Angle - Side)".

Answer:

$\angle BDC\cong\angle BEA$ Reason: Given; $\overline{CD}\cong\overline{AE}$ Reason: Given; $\angle B\cong\angle B$ Reason: Reflexive Property of Congruence; $\triangle ABE\cong\triangle CBD$ Reason: AAS (Angle - Angle - Side)