Question

question 9 of 10 based only on the given information, it is guaranteed that $overline{ab}perpoverline{cd}$. given: $\triangle abc$, $overline{ad}congoverline{bd}$, $overline{ac}congoverline{bc}$, $overline{cd}congoverline{cd}$. a. true b. false

Explanation:

Step1: Prove triangle congruence

In $\triangle ACD$ and $\triangle BCD$, we have $\overline{AD}\cong\overline{BD}$, $\overline{AC}\cong\overline{BC}$, and $\overline{CD}\cong\overline{CD}$ (by the SSS - Side - Side - Side congruence criterion). So, $\triangle ACD\cong\triangle BCD$.

Step2: Analyze corresponding angles

Since $\triangle ACD\cong\triangle BCD$, then $\angle ADC\cong\angle BDC$. Also, $\angle ADC+\angle BDC = 180^{\circ}$ (because they are a linear - pair of angles). So, $\angle ADC=\angle BDC = 90^{\circ}$.

Step3: Determine perpendicularity

If $\angle ADC = 90^{\circ}$, then $\overline{AB}\perp\overline{CD}$.

Answer:

A. True