Chapter 2.8, Problem 6PSA

To determine

Two given line segments are congruent.

Answer to Problem 6PSA

  $\text{Line segments }\overline{\text{FG}}\&\overline{\text{HJ}}\text{ are congruent }$

Explanation of Solution

Given information :

  $\text{Line segments }\overline{\text{FH}}\&\overline{\text{GJ}}\text{ are congruent }$ i.e., $\overline{\text{FH}}\cong \overline{\text{GJ}}$

Formula used :

Same shape and same size mean congruent Proof :

  $\begin{array}{l}\text{Since, given}\\ \overline{\text{FH}}\cong \overline{\text{GJ}}\\ \therefore \overline{\text{FH}}=\overline{\text{GJ}}\left(\because \text{ both are congruent}\right)\end{array}$

From given figure, we have

  $\begin{array}{l}\overline{\text{FH}}=\overline{\text{FG}}+\overline{\text{GH}}\text{ and }\overline{\text{GJ}}=\overline{\text{GH}}+\overline{\text{HJ}}\\ \therefore \overline{\text{FG}}+\overline{\text{GH}}=\overline{\text{GH}}+\overline{\text{HJ}}\\ \Rightarrow \overline{\text{FG}}=\overline{\text{HJ}}\\ \text{Thus, }\overline{\text{FG}}\cong \overline{\text{HJ}}\end{array}$

Hence, Proved.