Chapter 7.3, Problem 5CYU

To determine

To check: whether the additional information in the given option would be enough to prove the given similarity.

Answer to Problem 5CYU

C. $\overline{AD}$ and $\overline{EB}$ are parallel.

Explanation of Solution

Given:

The given similarity is $\Delta ADC\sim \Delta BEC$

  

The given options are:

1. $\angle DAC$ and $\angle ECB$ are congruent.
2. $\overline{AC}$ and $\overline{BC}$ are congruent.
3. $\overline{AD}$ and $\overline{EB}$ are parallel.
4. $\angle CEB$ is a right triangle

Calculation:

The given similar triangle is $\Delta ADC\sim \Delta BEC$ . And this is only possible $\overline{AD}$ and $\overline{EB}$ are parallel.

Therefore, $\angle CAD\text{ and }\angle CDA$ is equal to the $\angle CBE\text{ and }\angle CEB$ , so that the triangle is similar by AA- similarity

Hence, the correct option is (C).