Chapter 4.6, Problem 23PPS

To determine

To prove:

  $\angle JHK\cong \angle MHL$ for the following figure in the form of the paragraph:

  

Explanation of Solution

Given information:

  

Proof:

Know that $\Delta HJM$ and $\Delta HKL$ is an isosceles and equilateral triangle. $\angle JKH$ and $\angle HKL$ are supplementary and $\angle HLK$ and $\angle MLH$ are supplementary. According to the definition of isosceles triangle theorem $\angle HJK\cong \angle HML$ . According to the definition of equilateral triangle; all sides and all angles are congruent as $\angle HLK\cong \angle LKH\cong \angle KHL$ and $\overline{HL}\cong \overline{HK}\cong \overline{KL}$ . According to congruent supplements theorem; $\angle JKH\cong \angle MLH$ since $\angle JKH,\angle HKL,\angle HLK$ and $\angle MLH$ are supplementary. Therefore, use the angle-angle- side (AAS) congruence postulate gets that $\Delta JHK\cong \Delta MLH$ . Know that corresponding parts of congruent triangles are congruent so, $\angle JHK\cong \angle MHL$

Hence proved