Chapter 11.2, Problem 10PPS

a.

To determine

Tocalculate : Measure of DC

Answer to Problem 10PPS

  $DC=26cm$

Explanation of Solution

Given information : $\Delta ABC\cong \Delta ADC,BC=26cm$

Calculation :

  $BC=26$ cm

  $\Delta ABC\cong \Delta ADC$

As the corresponding sides of the congruent triangles are equal,

  $DC=BC=26cm$

b.

To determine

To calculate : measure of $\angle BAC$

Answer to Problem 10PPS

  $\angle BAC=45°$

Explanation of Solution

Given information: $\Delta ABC\cong \Delta ADC$

Formula used : Sum of angles of a triangle is $180°$

Calculation :

In $\Delta ADC$ , $\angle ADC+\angle DAC+\angle DCA=180°$ (Sum of angles of a triangle is $180°$ )

Put $\angle ADC=90°,\angle DCA=45°$

  $\begin{array}{l}90°+\angle DAC+45°=180°\\ \Rightarrow \angle DAC=180°-90°-45°=45°\end{array}$

As $\Delta ABC\cong \Delta ADC$ and corresponding angles of the congruent triangles are equal,

  $\angle BAC=\angle DAC=45°$