Question

1. given that $overline{cb}perpoverline{bd}$, $overline{de}perpoverline{ec}$, $overline{bd}congoverline{ec}$, the ____ justifies the conclusion that $\triangle abdcong\triangle aec$.

sas postulate

aas theorem

sss postulate

asa postulate

Explanation:

Step1: Identify right - angles

Since $\overline{CB}\perp\overline{BD}$ and $\overline{DE}\perp\overline{EC}$, $\angle ABD=\angle AEC = 90^{\circ}$ (perpendicular lines form right - angles).

Step2: Identify common angle

$\angle A$ is common to both $\triangle ABD$ and $\triangle AEC$.

Step3: Identify equal side

Given $\overline{BD}=\overline{EC}$.
We have two angles and a non - included side equal. The AAS (Angle - Angle - Side) Theorem 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 Theorem