Manchester High School s1

Manchester High School Geometry Midterm REVIEW

E 20 in F 1. Find the area of the rectangle EFGH. 25in

Use Pythagorean theorem H G Answer: 300 sq. in.

m• A 2. Which is a group of coplanar points? • W a) W,X,Y,Z l b) A,W,Y,Z • X c) B,W,X,Y Y • Z • d) A,B,Y,Z B

3. Points S,T, and W are collinear, with W between S and T. Find SW if ST = 52 and WT = 27.

Answer: 25 R • 4. WR and WT are opposite rays, as are WS and WV. S W • Which angle forms a linear pair with ∠TWU? V Answer: Angle RWU • U • • T

QuestionQuestions 4 9 & 10 5. Which point is in the exterior of ∠AXB? • F B • A • • C Answer: Point E, C or D • E • X D QuestionQuestions 5 12 & 13

A • 6. If the m ∠DAE = 65 and m∠DAF = 132, find m∠EAF. F B • C • • Answer: 67 D • E

7. Find m∠2 given that m∠1 = 33, m∠3 = 19, and m∠RTV = 105. S • • Answer: 53 U R 1 • 2 3 • V T Question 7 Manchester High School Geometry Midterm REVIEW

In the figure l ∣∣‌ ‌‌ m, and n and p are transversals. l m 8 7 10 9 5 6 n 8. Which type of angles are 8 and 10? ∠ ∠ 1 2

3 Answer: Corresponding 4 p 9. If m 7 = 9x +5 and m 9 = x +37, find the value of x. ∠ ∠ QuestionQuestions 8-9 54 - 56 Questions 46 - 48 9x + 5 = x + 37 8x = 32 x = 4

Given: m 6 = 67 and l m 10.What is the m∠7? 113 ∠ ∣∣ t 1 8 2 7 m 11.Find m∠4. 3 6 4 5 l

Answer: 67 Questions 10-11

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? 6 a) m1 = 50, m2 = 130, m3 = 50 b) m1 = 50, m2 = 130, m3 = 130 c) m1 = 130, m2 = 50, m3 = 50 1 130 d) m1 = 130, m2 = 50, m3 = 130 5 3 75 2 4

C 16. What is the measure of ABC? A B D ◀ E F H Answer: 79 ◀ 101 17. The circumference of a circle is 84 cm. Find the diameter and the radius. G Manchester High School Geometry Midterm REVIEW

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 =452.16 sq.cm a. b. 24 cm. C = 75.36 cm 15 in.

12 in. P = 36 in A = 54 sq. in

c. All angles are right angles in the figure at the right 10 ft. 2 ft. 7 ft. CHECK A = 109 sq. ft P = 56 feet 9 ft.

20. What is WX? 16 ft. 4 ft. a.W X Y Z

Y is mid point of WZ X is mid point of WY YZ = 10.5 cm. WX = 5.25 cm.

90 m

Given : m ∥ n 21. n

(2x + 10) What is x? x = 40 Manchester High School Geometry Midterm REVIEW

3 Write an equation of a line that is parallel to y = x + 9 and goes through the point (16, 30). 4 30 = ¾ (16) + b 30 = 12 + b 18 = b New equation y = ¾ x + 18 1 22. Write an equation of a line that is perpendicular to y = x -10 and goes through point (-4, -9).\ 3 -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.

2.5 cm Answer: The rectangle area is 18.75 sq. cm The semicircle is: 7.5 cm. ½(3.14)(3.752) =22.1 sq. cm Total area = 40.85 sq. cm Manchester High School Geometry Midterm REVIEW

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.

Length of pendulum hanging below = 6 inches. The tip of the pendulum sweeps the path shown, making a semicircle.

Bottom of clock Answer: The radius of the sweep is 6 inches, so the area of the semicircle is: ½ (3.14) 62 = 56.52 sq. inches

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 UXB . Find m UXY .

4r + 1 = 3r + 7 r = 6 so angle UXY = 3(6) + 7 = 25 Manchester High School Geometry Midterm REVIEW

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 m 2 is 65 because: Incoming/Outgoing 5 The m 3 is 65 because: Alternate Interior The m 4 is 65 because : Incoming/Outgoing 4 The m 5 is 25because it completes a triangle 3

33. Find the area of a rectangle with length of 5.4 in and width of 3.7 in. Manchester High School Geometry Midterm REVIEW

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) Manchester High School Geometry Midterm REVIEW