Chapter 12.5, Problem 5E

To determine

To show: Whether enough information is given to prove that the triangles are congruent using the HL Congruence Theorem.

Answer to Problem 5E

Yes, the information is enough to prove that two triangles are congruent.

Explanation of Solution

Given information:

  

Formula used:

The Hypotenuse-Leg Congruence Theorem

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle , then the two triangles are congruent.

Calculation:

According to the question,

There are two triangles $△ABC\text{ and }△FED\text{.}$

Now,

Statements	Reasons
H  1. $\overline{AC}=\overline{FD}$   2. $\overline{AB}\perp \overline{BC}$ , $\overline{FE}\perp \overline{ED}$   3. $\angle B\text{ and }\angle E\text{ are right angles}\text{.}$   4. $△ABC\text{ and }△FED\text{ are right triangles}\text{.}$	1.Given 2. Given 3. Definition of $\perp$ lines. 4. Definition of a right triangle.
L  5. $\overline{AB}=\overline{FE}$   6. $△ABC\cong △FED$	5. Given 6. HL Congruence Theorem

Hence, there is enough information given to prove that the two triangles are congruent.