Manchester High School
Geometry Midterm
REVIEW
1. Find the area of the rectangle EFGH.
Use Pythagorean theorem
Answer: 300 sq. in.
2. Which is a group of coplanar points?
a) W,X,Y,Z
b) A,W,Y,Z
c) B,W,X,Y
d) A,B,Y,Z
3. Points S,T, and W are collinear, with W between S and T. Find SW if ST = 52 and WT = 27.
Answer: 25
4. WR and WT are opposite rays, as are WS and WV.
Which angle forms a linear pair with ∠TWU?
Answer: Angle RWU
5. Which point is in the exterior of ∠AXB?
Answer: Point E, C or D
6. If the m ∠DAE = 65 and m∠DAF = 132, find m∠EAF.
Answer: 67
7. Find m∠2 given that m∠1 = 33, m∠3 = 19, and m∠RTV = 105.
Answer: 53
In the figure l ∣∣ m, and n and p are transversals.
8. Which type of angles are ∠8 and ∠10?
Answer: Corresponding
9. If m∠7 = 9x +5 and m∠9 = x +37, find the value of x.
9x + 5 = x + 37
8x = 32
x = 4
10. What is the m∠7? 113
11. Find m∠4.
Answer: 67
12. Find the slope of the line passing through points at (0,5) and (-1,2)
-3/-1 = 3 Slope = 3
13. Which selection is correct for the network?
a) mÐ1 = 50, mÐ2 = 130, mÐ3 = 50
b) mÐ1 = 50, mÐ2 = 130, mÐ3 = 130
c) mÐ1 = 130, mÐ2 = 50, mÐ3 = 50
d) mÐ1 = 130, mÐ2 = 50, mÐ3 = 130
16. What is the measure of ÐABC?
Answer: 79
17. The circumference of a circle is Find the diameter and the radius.
C = 2∏r 84∏ = 2∏r 42 = radius. 84 = diameter
18. ∠ABC is an obtuse angle. Sketch ∠ABC and give a possible m∠ABC.
Answers will vary
19. Find the area, perimeter, circumference, or missing dimension for the figures below.
a.
c. All angles are right angles in the figure at the right
CHECK
20. What is WX?
a.
21.
What is x? x = 40
Write an equation of a line that is parallel to and goes through the point (16, 30).
30 = ¾ (16) + b
30 = 12 + b
18 = b
New equation y = ¾ x + 18
22. Write an equation of a line that is perpendicular to and goes through point (-4, -9).\
-9 = -3(-4) + b
-9 = 12 + b
-21 = b
New equation: y = -3x - 21
23. Find the cost of carpeting the 1st floor lobby of a museum. There are twelve rooms. Each room is 10 feet high and 15 feet long by 12 feet wide. Carpet is $22.50 a square yard, padding is $2.25 a square yard, and installation is $.75 a square foot.
Carpet is based on floor area: 15 X 12 = 180 sq. ft X 12 rooms = 2160 sq. feet
Divide 2160 by 9 to get square yards: = 240 square yards.
240 sq. yards @ $24.75/sq. yd (carpet plus padding) = $5940
Installation is $.75/sq. ft for 2160 sq. ft = $1620
Total cost = 5940 + 1620= $7560.00
24. Find the area of the figure below. Note: The figure is a rectangle and a semi circle.
A pendulum on a clock can only swing so to each side, as marked in the picture below. Find the area available to the clock pendulum.
27. Find the value of x and z.
The linear pairs add to 180
(8z + 12) + (4z + 12) = 180 (5x + 14) + (10x + 16) = 180
12z + 24 = 180 15x + 30 = 180
z = 13 x = 10
28. XY is the angle bisector of .
Find m.
4r + 1 = 3r + 7
r = 6 so angle UXY = 3(6) + 7 = 25
29. Find the value of x.
These are Alternate Interior angles and are congruent, so
5x - 10 = 2x + 50
3x = 60
\ x = 20
30. Write the slope of the line containing the points (3, -4) and (-2, 5).
9/-5
31. The endpoints of a segment have the coordinates (-2, 5) and (4, -6). Write the coordinates of the midpoint of the segment.
32. The measure of angle 1 is 65° because it was given.
The mÐ 2 is 65 because: Incoming/Outgoing
The mÐ 3 is 65 because: Alternate Interior
The mÐ 4 is 65 because : Incoming/Outgoing
The mÐ 5 is 25because it completes a triangle
33. Find the area of a rectangle with length of 5.4 in and width of 3.7 in.
Area = 5.4 X 3.7 = 19.98 sq. in.
34. Draw 4 collinear points A, B, C, and D.
35. Two distinct planes intersect. Describe their intersection. Draw a sketch to support your answer.
36. Lines m and k are parallel. The slope of line m is -⅔. What is the slope of line k?
The slope of line k is also -⅔.
37. Line c and d are perpendicular. The slope of line d is ⅝. What is the slope of line c?
The slope of line c is -8/5
38. NASA Dryden is 117 degrees longitude and 34 degrees latitude. NASA Ames is 122 degrees longitude and 37 degrees latitude. You can consider the longitude and latitude as a coordinate pair (latitude, longitude). What is the distance between these two locations?
Use the distance formula
39. Explain the Exterior Angle Theorem.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. (page 197 of your text)