Chapter 3, Problem 13RP

To determine

To Prove: The congruency of $\overline{OH}$ with respect to $\overline{KG}$

Explanation of Solution

Given information: $\overline{FG}\cong \overline{JH}$ , O is the mid-point of $\overline{MF}$ and K is the mid-point of $\overline{MJ}$ is provided in the question which will help to find the solution.

Formula used: Here, we are using the concept of Side Angle Side congruency.

Proof: Here, In $\Delta OFH$ and $\Delta KGJ$

OH = KJ ( $\because$ O and K is the mid-point of $\overline{MF}$ and $\overline{MJ}$ )

  $\angle F=\angle J$ (opposite angles of equal sides)

FG = JH (given)

Hence, $\Delta OFH\cong \Delta KGJ$ (by Side angle side congruency)

So, $\overline{OH}\cong \overline{KG}$ (corresponding parts of congruent triangles)