Question

question 17 of 40
if $overline{ad}congoverline{bd}$, which of the following relationships can be proved and why?
a. $\triangle acdcong\triangle bcd$, because of asa.
b. $\triangle acdcong\triangle bcd$, because of sas.
c. there is not enough information to prove a relationship.
d. $\triangle acdcong\triangle bcd$, because of as.

Explanation:

Step1: Identify equal sides

Given $AD = BD$. Also, $CD$ is common to both $\triangle ACD$ and $\triangle BCD$, so $CD=CD$.

Step2: Identify the included - angle

$\angle ADC=\angle BDC = 90^{\circ}$ (right - angles as shown by the perpendicular symbol). So, we have two sides and the included angle equal. By the Side - Angle - Side (SAS) congruence criterion, $\triangle ACD\cong\triangle BCD$.

Answer:

B. $\triangle ACD\cong\triangle BCD$, because of SAS.