Geometry All Around US

By: Jakob Linder
Period: 1
Mrs. Causey

Geometry All Around Us

On this website, it will consist of ten geometry related questions to help prepare for future test, exams, and quizzes. Enjoy!

Answer Key!

1.) x=14° (You can solve for x using the Angle Addition Postulate. You must set up an equation to solve for x. So, you will have 3x and 3x+6 (6x+6) on one side of the equation and 90° on the other side due to it being a right angle. Your equation should look like this *6x+6=90°* Solve the equation and x should come out to become 14°. )

2.) x=16 (Add up x (AB) and 3x (BC) equal to 64 (AC) Your equation should look like this *4x=64*. Divide by 4 on both sides and x should come out to be 16.)

3.) ∠1 ≅∠2 and ∠3 ≅∠4 (Due to being vertical angles, both of the pairs form opposite rays.)

4.) n=90° (You must use the formula to find a single interior angle which is (n-2) 180 divided by n. Plug in 4 for n due to a quadrilateral having 4 sides. After solving the problem, one alternate interior angle should equal 90°.)

5.) Parallel Lines (They are parallel because the lines will never intersect no matter the height of the two poles.)

6.) ∠6, ∠5, ∠2, ∠1 = 120° and ∠8, ∠7, ∠4, ∠3 = 60° (Since lines A and B are parallel, you can say angle one is congruent to angle six due to being alternate interior angles. Angle one is also a vertical angle with angle two, same with angles six and five. So, ∠6, ∠5, ∠2, ∠1 = 120°. Since lines A and B are parallel, you can say angle eight is congruent to angle three due to being alternate interior angles. Angle eight is also a vertical angle with angle seven, same with angles three and four. So, ∠8, ∠7, ∠4, ∠3 = 60°.)

7.) Right, Scalene (You can classify the triangle's angle by being a right angle due to it being a right angle. You can classify the triangle's sides due to being scalene due to all the sides not being congruent.)

8.) m∠A =50° (You solve for m∠A, by using the Exterior Angle Theorem. So set up the equation x + 75 (Combination of the Remote Interior Angles) equal to 3x - 25 (Exterior Angle). Your equation should look like this *x + 75 = 3x - 25* After solving the equation the m∠A should equal 50°)

9.) Segment DB (Segment DB is a segment from the vertex of the triangle that goes to the midpoint of the opposite side)

10.) SAS (Side AB≅DE and Side FD≅CA. ∠A≅∠D. Since ∠A and ∠D are both the included angle in both triangles, the only postulate that would prove the two triangles congruent is SAS.)

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