Chapter 4, Problem 12CT

To determine

Can two triangles be proved congruent? If so, name the method.

Answer to Problem 12CT

Yes, $\Delta ABC\cong \Delta DEC$ by HL method.

Explanation of Solution

Given:

The given figure is,

  

First name the triangles in the given figure,

  

Here, $\overline{AB}\cong \overline{DE},\overline{BC}\cong \overline{EC}$ and $m\angle ACB=m\angle DCE={90}^o$

Now,

In $\Delta ABC\text{and}\Delta DEC$

  $m\angle ACB=m\angle DCE={90}^o$ (given)

So they are right angle triangle.

Also,

  $\overline{AB}\cong \overline{DE}$ (hypotenuse) and

  $\overline{BC}\cong \overline{EC}$ (leg)

So,

Therefore, $\Delta ABC\cong \Delta DEC$ by HL method.