Chapter 3.5, Problem 2PSA

To determine

To prove: The given triangles are congruent.

Explanation of Solution

Given information:

In given two triangles FGH and JHG

  $\begin{array}{l}\angle \text{FGH is a right angle}\\ \angle \text{JHG is a right angle}\\ \overline{\text{FG}}\cong \overline{\text{JH}}\end{array}$

  

Formula used:

Same shape and same size objects are congruent

Common side in two triangles is always congruent

SAS criteria of congruency

Proof

  $\begin{array}{l}\text{In }\Delta \text{FGH and }\Delta \text{JHG},\text{we have}\\ \overline{\text{FG}}\cong \overline{\text{JH}}\mathrm{........}\text{Given}\\ \therefore \overline{\text{FG}}=\overline{\text{JH}}\mathrm{......}\text{by definition of congruency}\mathrm{.......}\left(i\right)\\ \overline{\text{GH}}=\overline{\text{GH}}\mathrm{.......}\text{common side}\mathrm{.........}\left(ii\right)\\ \angle \text{FGH = }\angle \text{JHG}\mathrm{......}\text{ given equal to 90}°\mathrm{......}\left(iii\right)\\ \text{From }\left(i\right),\left(ii\right)\text{ and }\left(iii\right),\text{we have}\\ \Delta \text{FGH }\cong \Delta \text{JHG}\mathrm{......}\text{SAS criteria of congruency is satisfie}\end{array}$