Chapter 4, Problem 15CR

To determine

To write: the proof in two columns method.

Explanation of Solution

Given information:

  $\overline{GH}\perp \overline{HJ};\overline{KJ}\perp \overline{HJ}$

  $\angle G\cong \angle K$

  

Calculation:

AAS Theorem: If two angles and non included side of a triangle is congruent to the corresponding parts of another triangle, then the triangles are said to be congruent.

  

Given:

  $\overline{GH}\perp \overline{HJ};\overline{KJ}\perp \overline{HJ}$

  $\angle G\cong \angle K$

Prove: $\Delta GHJ\cong \Delta KJH$

Proof:

Statements	Reasons
1. $\overline{GH}\perp \overline{HJ};\overline{KJ}\perp \overline{HJ}$	Given
2. $m\angle GHJ=90°;m\angle KJH=90°$	Definition of $\perp$lines
3. $\angle G\cong \angle K$	Given
4. $\overline{HJ}\cong \overline{HJ}$	Reflexive property
5. $\Delta GHJ\cong \Delta KJH$	AAS Postulate