Chapter 3.4, Problem 5PSA

To determine

To prove:In the given figure, Angle G and Angle H are congruent

Explanation of Solution

Given information :

In a circle with center O,

  $\overline{\text{GJ}}\cong \overline{\text{HJ}}$

Formula used :

Same shape and same size, by definition of congruency

RHS criteria of congruency

Congruent Part of Congruent Triangles are Congruent (CPCTC)

Proof :

Join J to O, as shown below

  $\begin{array}{l}\text{In }\Delta \text{s JOG and JOH, we have}\\ \overline{\text{GJ}}\cong \overline{\text{HJ}}\mathrm{..........}\text{Given}\\ \therefore \overline{\text{GJ}}=\overline{\text{HJ}}\mathrm{.......}\text{by definition of congruency}\\ \overline{\text{OG}}=\overline{\text{OH}}\mathrm{.........}\text{radii of circle }\\ \angle \text{JOG = }\angle \text{JOH = 90}°\\ \therefore \Delta \text{JOG}\cong \Delta \text{JOH}\mathrm{......}\text{RHS criteria of congruency is satisfied}\\ \text{⇒}\angle \text{G}\cong \angle \text{H}\mathrm{..........}\text{by cpctc}\end{array}$