Chapter 4.4, Problem 13WE

To determine

To prove: $\overline{JG}\cong \overline{MK}$ in two column method.

Explanation of Solution

Given information:

Given figure,

Given,

$M$ is the midpoint of $\overline{JK}$ ;

  $\angle 1\cong \angle 2$

Calculation:

The Isosceles Triangle Theorem: If Two angles are congruent, then the sides opposite to those angles are congruent.

Given: $M$ is the midpoint of $\overline{JK}$ ;

  $\angle 1\cong \angle 2$

Prove: $\overline{JG}\cong \overline{MK}$

Proof:

Statements	Reasons
1. $\angle 1\cong \angle 2$	Given
2. $\overline{JG}\cong \overline{JM}$	Converse of isosceles theorem
3. $M$ is the midpoint of   4. $\overline{JK}$	Given
5. $\overline{JM}\cong \overline{MK}$	Definition of midpoint
6. $\overline{JG}\cong \overline{MK}$	Transitive property