Chapter 7, Problem 2CT

(a)

To determine

To Find: The missing value with the help of given condition.

Answer to Problem 2CT

The missing value is $\angle U\cong \angle C$

Explanation of Solution

Given information:

If $quad.ABCD~quad.THUS$ .

Consider two quadrilaterals, ABCD and THUS.

  $quad.ABCD~quad.THUS$

As the given quadrilaterals are similar, therefore, their corresponding angles should be congruent.

  $\begin{array}{cc}& \angle A\cong \angle T\\ & \angle B\cong \angle H\\ & \angle C\cong \angle U\\ & \angle D\cong \angle S\\ & \text{From equation (1),}\\ & \angle U\cong \angle C\\ & \end{array}$

Hence, $\angle U\cong \angle C$ .

(b)

To determine

To Find: The missing value with the given condition.

Answer to Problem 2CT

  $\frac{BC}{HU}=\frac{AD}{TS}$

Explanation of Solution

As the given quadrilaterals are similar, therefore, their corresponding sides should be in proportion.

  $\begin{array}{cc}& \frac{AB}{TH}=\frac{BC}{HU}=\frac{CD}{US}=\frac{AD}{TS}\dots \dots \\ & \text{From equation (2),}\\ & \frac{BC}{HU}=\frac{AD}{TS}\\ & \end{array}$

Hence, $\frac{BC}{HU}=\frac{AD}{TS}$