Question

question 6 of 33 if ad ≅ bd, which of the following relationships can be proved and why? a. there is not enough information to prove a relationship. b. △acd ≅ △bcd, because of sas. c. △acd ≅ △bcd, because of as. d. △acd ≅ △bcd, because of asa.

Explanation:

Step1: Identify given information

We know that $\overline{AD}\cong\overline{BD}$, and $\angle ADC = \angle BDC=90^{\circ}$ (right - angles) and $\overline{CD}=\overline{CD}$ (common side).

Step2: Recall congruence postulates

The Side - Angle - Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in $\triangle ACD$ and $\triangle BCD$, $AD = BD$ (given), $\angle ADC=\angle BDC$ (both are right - angles) and $CD$ is common to both triangles.

Answer:

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