Chapter SH, Problem 11.2.3EP

To determine

triangles shown are congruent or not.

Answer to Problem 11.2.3EP

  $△ABC$ and $△DEF$ are not 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:

  $\begin{array}{l}\angle B\cong \angle E\left(\sin glearc\right)\\ \angle C\cong \angle F\left(twoarc\right)\\ \angle A\cong \angle D\left(threearc\right)\end{array}$

From the given figure, the corresponding sides are,

  $AC\ne DF$ (as $AC=21km,DF=63km$ )

  $BC\ne EF$ (as $BC=18km,EF=54km$ )

Since the corresponding sides of triangle $△ABC$ and $△DEF$ are not congruent so the two triangles $△ABC$ and $△DEF$ are not congruent.