Question

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

sas postulate

aas theorem

asa postulate

hl theorem

Explanation:

Step1: Identify right - angled triangles

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

Step2: Analyze given congruent parts

We are given that $\overline{CB}\cong\overline{DE}$. Also, $\overline{CD}$ is the hypotenuse for both right - angled triangles $\triangle BCD$ and $\triangle EDC$ and is common to both, so $\overline{CD}\cong\overline{CD}$.

Step3: Apply congruence criterion

For right - angled triangles, when one leg and the hypotenuse of one right - angled triangle are congruent to one leg and the hypotenuse of another right - angled triangle, we use the HL (Hypotenuse - Leg) Theorem.

Answer:

HL Theorem