Geometry Homework (Due 09/17/2015)
1. Prove that: m<1 + m<6 = 180
2. Given that: m<2 = 3x, m<7 = 2x – 20, and m<8 = 4y, find x,y, and all angles.
Explain every condition and step.
3. Prove that: m<5 + m<7 + m<12 = 180
a) using the 1-2-3 straight angle.
b) using the 4-5-6 straight angle.
c) using the 2-3-4 straight angle.3
d) using the 3-4-5 straight angle.
4. Prove that the sum of the interior angles of a triangle is 180.
5. Given that m<α = 5x + 30, m<β = 7x-10, and m<γ = 10x – 60, find x and the
measures of all angles. Explain every condition and step.
6. Prove that: m<δ = m<α + m<β.
7. Prove that: m<δ = m<α + m<β.
8. Prove that an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles of the triangle.
9. Given that m<β = 55, and m<δ = 160, use 8 to find the measure <α. Explain every
condition and step.
10. Given the parallelogram bellow, prove that:
a) m<1 = m<4
b) m<2 = m<3
11. Prove that a parallelogram has opposite angles congruent.
12. Given m<1 = 10x + 50, m<2 = 10y-20, and m<4 = 5x + 90, find x,y, and the
measure of all angles. Explain every condition and step.
13. Given that m<3 = 40, and m< 17 = 108, find m<16.
14. Given m<3 = 50, find all angles.
15. Find the sum of the interior angles of a pentagon, without using any formula.
16. Find the sum of the interior angles of a hexagon, without using any formula.
17. Repeat exercises 10, 11, 3 and 4, using the formula S=(n-2)180, where n is the
number of polygon’s sides. Compare the results.
18. Use the formula of 17 to find S for a decagon and a quadrilateral.
19. Bisect a line segment.
20. Bisect an angle.
21. Add and subtract two line segments.
22. Construct a congruent angle to a given angle.
23. Add and subtract two angles.
24. Construct a parallel to a line, from a given point, which is not on the line. (All
three methods).
25. Construct a perpendicular to a line from a given point, which is not on the line.
26. Divide a line segment in three equal parts.
27. Divide a line segment in five equal parts.
28. (Challenge). Find the sum of the exterior angles of a
a)pentagon,
b)hexagon,
c) any polygon.
29. (Challenge). Use 28 to prove the formula of 17.