Chapter 4.3, Problem 34PPS

(a)

To determine

The two polygons used to create the pattern.

Answer to Problem 34PPS

Triangles and hexagons.

Explanation of Solution

Given:

The pattern is made using regular polygons.

  

Calculation:

The two polygons that are used to create the given pattern are triangles and hexagons.

(b)

To determine

The pair of congruent triangles.

Answer to Problem 34PPS

  $\Delta ABC\cong \Delta DEC.$

Explanation of Solution

Given:

The pattern is made using regular polygons.

  

Calculation:

According to the given figure;

  $\Delta ABC\cong \Delta DEC.$

(c)

To determine

The pair of corresponding angles.

Answer to Problem 34PPS

  $\angle B\text{ and }\angle \text{E}$ are corresponding angles.

Explanation of Solution

Given:

The pattern is made using regular polygons.

  

Calculation:

According to the given figure;

  $\angle B\text{ and }\angle \text{E}$ are corresponding angles.

(d)

To determine

The length of AE.

Answer to Problem 34PPS

  $AE=4\text{ inches}$

Explanation of Solution

Given:

The pattern is made using regular polygons.

  

  $CB=2\text{ inches}\text{.}$

Calculation:

All sides have equal length as the given figure is made of regular polygons.

Hence, $AC=2\text{ in and CE = 2 in}\text{.}$

Therefore;

  $\begin{array}{l}AE=AC+CE\\ AE=2+2\\ AE=4\text{ inches}\end{array}$

(e)

To determine

The measure of angle D.

Answer to Problem 34PPS

  $m\angle D=60.$

Explanation of Solution

Given:

The pattern is made using regular polygons.

  

Calculation:

In a regular triangle, each angle is equal. So, the measure of every angle in an equiangular triangle is 60.

Hence, $m\angle D=60.$