Chapter 3.2, Problem 9PSA

To determine

To prove : The congruency of $\Delta PBA\cong \Delta PBC$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{PA}\cong \overrightarrow{PC}$

  $\overrightarrow{BA}\cong \overrightarrow{BC}$

Formula used : We can say that any two given triangles are congruent if all three sides of both of those triangles are equal

Proof : As the chord PB is a common shared chord in both triangles, we can say that

  $\overrightarrow{PA}\cong \overrightarrow{PC}$

  $\overrightarrow{BA}\cong \overrightarrow{BC}$

  $\overrightarrow{PB}\cong \overrightarrow{PB}$

From the given information we can say that in $△PBA$ and $△PBC$ , all three sides are given to be congruent

Hence, by the formula mentioned above, both of the triangles are congruent

Thus,

  $\Delta PBA\cong \Delta PBC$