Chapter 7, Problem 18CP

To determine

To find: The statement which is not necessarily true.

Answer to Problem 18CP

The statement G. $\overline{\text{AC}}\cong \overline{\text{DF}}$ is not necessarily true.

Explanation of Solution

Given information: Given, $\Delta \text{ABC}\sim \Delta \text{DEF}$ , which statement is not necessarily true?

Calculation:

Since, $\Delta \text{ABC}\sim \Delta \text{DEF}$ ,then they are similar.

Let’s find the relations of similar triangles $\angle \text{A}\cong \angle D\text{ , }\angle \text{B}\cong \angle E\text{ and }\angle \text{C}\cong \angle \text{F}$

And, $\overline{\text{AB}}\cong \overline{\text{DE}},\overline{\text{AC}}\cong \overline{\text{DF}},\text{ and }\overline{\text{BC}}\cong \overline{\text{EF}}$

Also, $\frac{\text{AB}}{\text{DE}}=\frac{\text{AC}}{\text{DF}}=\frac{\text{BC}}{\text{EF}}$ .

Hence, The statement G. $\overline{\text{AC}}\cong \overline{\text{DF}}$ is not necessarily true.