Chapter 3.5, Problem 3PSA

To determine

To prove: Two given triangles are congruent

Explanation of Solution

Given information In two given triangles PSM and ORM

  $\overline{\text{PM}}\cong \overline{\text{RH}}$

  $\angle \text{PSM }\cong \angle \text{ORM}$

Formula used Proof

  $\begin{array}{l}\text{In }\Delta \text{PSM and }\Delta \text{ROM},\text{we have}\\ \overline{\text{PM}}\cong \overline{\text{RH}}\mathrm{.......}\text{Given}\\ \therefore \overline{\text{PM}}=\overline{\text{RH}}\mathrm{.....}\text{by definition of congruency}\mathrm{......}\left(i\right)\\ \angle \text{SPM }\cong \angle \text{ORM}\mathrm{......}\text{ given }\\ \therefore \angle \text{SPM =}\angle \text{ORM}\mathrm{...}\text{ by definition of congruency}\mathrm{....}\left(ii\right)\\ \overline{\text{SM}}=\overline{\text{OM}}\mathrm{.....}\text{sides opposite to equal angles}\mathrm{..........}\left(iii\right)\\ \text{From }\left(i\right),\left(ii\right)\text{ and }\left(iii\right),\text{we have}\\ \Delta \text{PSM }\cong \Delta \text{ORM}\\ \text{Hence proved}\end{array}$