Geometry All Around Us

Aashi Agarwala

Question #1

Find the value of x.

Question #2

This is a regular polygon. What is the sum of all of the interior angles in this polygon?

Question #3

To prove these lines parrallel, what proof can you use?

Question #4

What postulate can you use to prove these triangles congruent?

Question #5

What postulate can you use to prove these triangles congruent?

Question #6

The two pink lines are parallel. Find 'x' using all of the information given in the picture below.

Question #7

The two triangles are right. What postulate can you use to prove these triangles congruent?

Question #8

The triangle below is an isosceles. Find the value of x.

Question #9

The sum of all interior angles in this octagon is 1,080. What is the formula used to come up with the sum of all interior angles in a polygon?

Question #10

Are the two triangles similar? If so, state the postulate you can use to prove the triangles similar.

Answers!

  1. x=120. The two angles create a straight angle, which equals 180 degrees To get the answer you must subtract the measure of the other angle given, in this case it is 60, from 180. 180-60=120
  2. 720. The polygon shown was a hexagon because it had 6 sides. To find the sum of all of the interior angles you must you the formula, (n-2)*180. You must replace n for the number of sides, in this case it is 6. (6-2)*180=(4)*180=720.
  3. Alternate Exterior Angles. The pink line is the transversal. The 2 congruent angles are outside the 'parallel lines' and are on opposite sides of the transversal. Therefore you can use the Alternate Exterior postulate to prove the lines parallel.
  4. Angle Angle Side. 2 corresponding angles are congruent because it is given in the picture. Also, another pair of corresponding angles are congruent because it is given in the picture. You can find that the sides are congruent using the reflexive postulate because they both share that side. Therefore, you can conclude that the triangles are congruent using AAS.
  5. Hypotenuse Leg. The triangles are right because it was given. The hypotenuses was congruent because it was given. The legs are congruent because it was given. Therefore, you can conclude the triangles are congruent using the HL postulate.
  6. x=100. The two lines are parallel. however, in order to make this true, the two consecutive interior angles must add up to be 180. You must subtract the measure of the angle given, in this case it is 80, from 180. 180-80=100
  7. Hypotenuse Leg. The two triangles are right because it is given. The two hypotenuses are congruent because it is given. You can conclude that the legs are congruent using the reflexive property because they both share that side
  8. x=80. The triangle was an isosceles, so the base angles must be congruent. There are a total of 180 degrees in a triangle. One of the base angle's measure was 50 degrees The other base angle must be 50 degrees too because it is an isosceles triangle. To find x, we must subtract the total of the other two angles, in this case it is 100 (50+50=100), from 180. 180-100=80
  9. (n-2)*180 =sum of all interior angles in a polygon
  10. The triangles are similar. You can use SAS to prove them similar. The sides are proportional. You know this because if you find the scale factor of each line, you will find that they are the same. 9/3=12/4. You know that one of the angles are congruent using the reflexive proprerty becasue they both share that angle.

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