# "Geometry All Around Us"

### By Nico Nettemeyer

### Answers are at the bottom.

## Problem 1

Find the measure of angles one, two, and three using the given information.

## Problem 2

Using the given information, solve for "x".

## Problem 3

What type of lines are shown with the two street signs?

## Problem 4

Find the distance between the two red points.

## Problem 5

Find the measure of the unknown variable (w).

## Problem 6

**Not Drawn To Scale**

Is triangle BAC congruent triangle BDC and/or is triangle BAC ~ triangle BDC?

What postulate would be used to prove that the triangles are congruent and/or similar?

## Problem 7

What is the sum of all interior angles in this polygon? What is the measure of one exterior angle of this regular polygon?

## Problem 8

What type of triangle is shown above?

## Problem 9

If the lengths of the two sides of the triangle are 6 and 10, find the two numbers that the length of the third side must fall between.

A.) 6 < x < 10

B.) 6 < x < 16

C.) 4 < x < 10

D.) 4 < x < 16

## Problem 10

What postulate would prove the two touchlines (sidelines) parallel?

## Answers

1.) M<1 = 58 degrees, M<2 = 122 degrees, M<3 = 58 degrees

2.) X is equal to 20.5

3.) Skew Lines

4.) 82

5.) 143 degrees

6.) The triangles are congruent and similar. The postulate used was SAS.

7.) 1080 degrees and 45 degrees

8.) Acute, Scalene

9.) Answer D

10.) Alternate Interior