Question

question 10 of 10
based only on the given information, it is guaranteed that $overline{ac}congoverline{bc}$.
given: $\triangle abc$
$overline{ab}perpoverline{cd}$
$angle acdcongangle bcd$
a. true
b. false

Explanation:

Step1: Consider right - angled triangles

In $\triangle ACD$ and $\triangle BCD$, $\angle ADC=\angle BDC = 90^{\circ}$, $\angle ACD=\angle BCD$, and $CD = CD$ (common side).

Step2: Use ASA congruence

By Angle - Side - Angle (ASA) congruence criterion, $\triangle ACD\cong\triangle BCD$.

Step3: Get corresponding sides

Since the triangles are congruent, $AC = BC$ (corresponding sides of congruent triangles).

Answer:

A. True