# Geometry All Around Us!

### By Aala Nasir

# Question #1

Given the measurements above, can you find the measurement of angle x? Can you find the measurement of angle y? Answer: x=88 degrees

y=42 degrees, due to the Exterior Angle Theorem, which states that the sum of the measures of the remote interior angles will equal the measure of the exterior angle.

# Question #2

Given that the fences are parallel and that the one in the middle is the transversal, find the measurement of angle x. What type of angles is represented above?

Answer: 108 degrees; alternate interior angles (In order for two lines to be parallel, the measure of the alternate interior angles must be equal.)

# Question #3

Given the measurement above, find the measurement of angle x and y. What type of angles are represented above?

Answer: x=84 degrees; y=96 degrees; vertical angles (To solve this, first you would need to subtract 96 from 180 and the difference is 84. Remember, the measures of vertical angles are equal, therefore x=84 degrees and y=94 degrees)

# Question #4

Given the measurements of all three angles, list the sides in order from longest to shortest.

Answer: Line b, Line c, Line a (The larger angle will be opposite of the longest side and the smaller angle will be opposite of the shortest side.)

# Question #5

Find the sum of all the exterior angles in the polygon above.

Answer: 360 Degrees

# Question #6

What is represented on the ceiling of the building above?

Answer: Tessellation (using triangles.)

# Question #7

What type of lines do the signs above represent? (parallel, oblique, skew, perpendicular)

Answer: Skew lines! This is because the the signs are not intersecting, nor are they parallel.

# Question #8

In order to prove the triangles above congruent, what postulate would you use?

Answer: Side Angle Side Postulate. (SAS)

# Question #9

What is the sum of all the interior angles above? What is the measure of one interior angle?

Answer: 1080 degrees; 135 degrees

# Question #10

What type of triangle is shown above?

Answer: Obtuse, Isosceles