Chapter SH, Problem 11.2.4EP

To determine

triangles shown are congruent or not.

Answer to Problem 11.2.4EP

  $△JIH$ and $△MLK$ are congruent.

Explanation of Solution

Given information:

  

Calculation:

For completing the congruence statement,

If two triangles are congruent then their corresponding angles and their corresponding sides are congruent.

From figures, corresponding angles are:

  $\begin{array}{l}\angle J\cong \angle M\left(\sin glearc\right)\\ \angle I\cong \angle L\left(twoarc\right)\\ \angle H\cong \angle K\left(threearc\right)\end{array}$

From the given figure, the corresponding sides are,

  $JI=ML\left(JI=6km,ML=6km\right)$

  $HJ=KM\left(HJ=5km,KM=5km\right)$

Since the corresponding sides of triangle $△JIH$ and $△MLK$ are congruent so the two triangles $△JIH$ and $△MLK$ are congruent.