# Geometry all Around Us

**Project by: Claude Owen, Period 1, 1/21/14**

## Question 1

The two lines indicated are parallel. The lines have been extended for easier viewing. What is the relationship between angles 1 & 3?

## Question 2

Are these two street signs perpendicular, parallel, or skew?

## Question 3

What is the measure of one of the exterior angle on this stop sign?

## Question 4

Using the above picture, identify which postulate of congruent triangles you can use to prove these two triangles congruent. (Not drawn to scale)

## Question 5

Find the measure of all the interior angles.

## Question 6

The two triangles above are congruent. Which postulates could you use to prove this fact?

## Question 7

Using the above picture, and your knowledge of the Triangle Inequality Theorem, can you prove that the shape indicated is an existing triangle? Why or why not?

## Question 8

Do all of these shapes tessellate? If so, what shapes do they make?

## Question 9

In the figure, which two triangles are right triangles?

## Question 10

Line AB is a bisector of angle DAC. What construction of geometry does this demonstrate an example of?

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## ANSWERS:

Question 1.) The relationship between angles 1 & 3 is that they are vertical angles.

Question 2.) The two signs are perpendicular to one another.

Question 3.) Since we know that the measure of all exterior angles in a polygon is 360 degrees, divide 360 by 8, and because it is an octogon, you will get 45 degrees for each exterior angle.

Question 4.) You can use the Side, Side, Side (SSS) postulate to prove these two triangles are congruent.

Question 5.) The measure of all of the interior angles is 720 degrees. Use the interior angle formula for this problem, which is 180(n-2).

Question 6.) You could use the triangle postulate of HL (hypotenuse, leg), or SAS (Side, Angle, Side) Either of the two postulates could have been used.

Question 7.) Yes, the shape indicated is a triangle. We know this because as long as any of the two sides are longer than the third side, a triangle exists.

Question 8.) They do tessellate, and they are rhombuses.

Question 9.) ▲ADC, and ▲ADB are the right triangles.

Question 10.) This is an example of an angle bisector.