Chapter 3.2, Problem 3PSA

To determine

To prove : The congruency of $\Delta ABD\cong \Delta CBD$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{AB}\cong \overrightarrow{CB}$

  $\angle ABD\cong \angle CBD$

Formula used : Two triangles are congruent by Side-angle-side property, if there are two congruent sides, and the angle between them is also congruent

Proof : we know that $\overrightarrow{AB}\cong \overrightarrow{CB}$ , and $\angle ABD\cong \angle CBD$

Now, we can also see that there is a common side BD between them. Hence, now we can say that

  $\overrightarrow{AB}\cong \overrightarrow{CB}$

  $\angle ABD\cong \angle CBD$

  $\overrightarrow{BD}\cong \overrightarrow{BD}$

Thus, now by using the SAS property as mentioned above, we can say that two triangles are congruent

Hence, proved that $\Delta ABD\cong \Delta CBD$