Chapter 12.5, Problem 24E

a.

To determine

To show: The additional information to prove $△ABC\cong △CDE$ by SSS Congruence Theorem.

Answer to Problem 24E

The additional information is $AB\cong \text{ CD}$ .

Explanation of Solution

Given information:

  

  $\overline{BC}\cong \overline{DE}\text{ and }\overline{AC}\cong \overline{CE.}$

Formula used:

Side-Side-Side Congruence Theorem

If three sides of one triangle are congruent to three sides of a second triangle, then two triangles are congruent.

Calculation:

According to the question,

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

Now,

The additional information to prove $△ABC\cong △CDE$ is :-

The side should be equal.

  $AB\cong \text{ CD}$

Hence, the additional information is $AB\cong \text{ CD}$ .

b.

To determine

To show: The additional information to prove $△ABC\cong △CDE$ by HL Congruence Theorem.

Answer to Problem 24E

The additional information is $\angle CBA\cong \angle \text{EDC}={90}^{\circ }.$

Explanation of Solution

Given information:

  

  $\overline{BC}\cong \overline{DE}\text{ and }\overline{AC}\cong \overline{CE.}$

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 $△ABC\text{ and }△CDE\text{.}$

Now,

Statements	Reasons
H 1. $\overline{AC}=\overline{CE}$	1.Given
L 5. $\overline{BC}=\overline{DE}$	5. Given

The additional information to prove $△ABC\cong △CDE$ is :-

There should be right angles.

Such that $\overline{BC}\perp \overline{AB}\text{ and }\overline{ED}\perp \overline{DC}$

  $\angle CBA\cong \angle \text{EDC}={90}^{\circ }.$

Hence, the additional information is $\angle CBA\cong \angle \text{EDC}={90}^{\circ }.$