Question

1. given that $overline{cb}perpoverline{bd}$, $overline{de}perpoverline{ec}$, $overline{cb}=overline{de}$, the ____ justifies the conclusion that $\triangle bcdcong\triangle edc$.

hl theorem
asa postulate
sas postulate
aas theorem

Explanation:

Step1: Identify right - angled triangles

Since $CB\perp BD$ and $DE\perp EC$, $\triangle BCD$ and $\triangle EDC$ are right - angled triangles.

Step2: Recall triangle congruence postulates

The Hypotenuse - Leg (HL) Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent. Here, $CD$ is the common hypotenuse for $\triangle BCD$ and $\triangle EDC$, and $CB = DE$ (given).

Answer:

A. HL Theorem