Question

question 7 of 10
based only on the given information, it is guaranteed that \\(overline{ac}\cong\overline{bc}\\).
given: \\(\triangle abc\\)
\\(\overline{ab}\perp\overline{cd}\\)
\\(\angle acd\cong\angle bcd\\)
a. true
b. false

Explanation:

Step1: Analyze the triangles

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

Step2: Use the AAS (Angle - Angle - Side) congruence criterion

By the AAS congruence criterion, \(\triangle ACD\cong\triangle BCD\).

Step3: Conclude the equality of sides

If \(\triangle ACD\cong\triangle BCD\), then \(AC = BC\) (corresponding parts of congruent triangles are congruent), so \(\overline{AC}\cong\overline{BC}\).

Answer:

A. True