Chapter 12.5, Problem 6E

To determine

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

Answer to Problem 6E

No, the information is not 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 $△PQT\text{ and }△SRT\text{.}$

Now recall that the side opposite the right angle is called the hypotenuse of the right angle.

In both the triangles right angle is at T.

The opposite side will be $PQ\text{ and }RS$ of $△PQT\text{ and }△SRT\text{ respectively}\text{.}$

Therefore, the opposite sides are not equal.

Hence, the information is not enough to prove that the two triangles are congruent.