Chapter 2, Problem 2RP

To determine

To Prove: In the given figure $\overline{PT}\cong \overline{PS}$

Explanation of Solution

Given information : According to the figure we are given $\overline{PV}\cong \overline{PR}\text{ , }\overline{VT}\cong \overline{RS}$

Formula used : Congruent parts added in other congruent parts, make the sum also congruent

Proof: As per the question we have $\overline{PV}\cong \overline{PR}\mathrm{.........................}\text{(i)}$

and $\overline{VT}\cong \overline{RS}\mathrm{................................................}\text{(ii)}$

also $\overline{PV}\text{ + }\overline{VT}\text{ = }\overline{PT}\mathrm{............................................}\text{(iii)}$

  $\overline{PR}\text{ + }\overline{RS}\text{ = }\overline{PS}\mathrm{...............................................}\text{(iv)}$

As (i) and (ii) are congruent so if they will be added their respective sums also will be congruent.

So, adding (i) and (ii) we will get:

  $\begin{array}{l}\overline{PV}\text{ + }\overline{VT}\cong \overline{PR}\text{ + }\overline{RS}\\ \\ \Rightarrow \overline{PT}\cong \overline{PS}\mathrm{..........................................}\text{(from (iv) and (v))}\end{array}$

Which proves the required result.