Chapter 10.3, Problem 15Q

(a).

To determine

The reason of shortest bar parallel to longest bar.

Explanation of Solution

Given:

Proof:

In the given description,

All bars are parallel to each bars next to them.

Suppose,

If two given lines m and n are parallel to a line l.

Then,

According to parallel line transitive property, they are parallel to each other.

i.e.,

  $\begin{array}{l}l\parallel m\text{and}l\parallel n\\ \therefore m\parallel n\end{array}$

Therefore,

Shortest bar is parallel to longest bar.

(b).

To determine

The line m and n are parallel

Answer to Problem 15Q

  $\angle 1\text{=}\angle 2=58°$

Explanation of Solution

Given:

  $\angle 1\text{=}58°$

Solution:

In the given description,

All bars are parallel to each bars next to them.

Suppose,

If two given lines m and n are parallel to a line l.

Then,

According to parallel line transitive property, they are parallel to each other.

i.e.,

  $\begin{array}{l}l\parallel m\text{and}l\parallel n\\ \therefore m\parallel n\end{array}$

Therefore,

Angle 1 and angle 2 are equal by the property of corresponding angle.

  $\angle 1\text{=}\angle 2=58°$

a. Explain why the tallest bar is parallel to the shortest bar.

b. Imagine that the left side of each bar extends infinitely as a line. If $m\angle 1=58°$ , then what is $m\angle 2$ ?