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Manchester High School Geometry Midterm REVIEW E 1. Find the area of the rectangle EFGH. Use Pythagorean theorem 20 in F 25in H G Answer: 300 sq. in. m• 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 A •W X • Y l •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 S 4. WR and WT are opposite rays, as are WS and WV. Which angle forms a linear pair with ∠TWU? Answer: V Angle RWU W • • •T • U Questions Question9 4& 10 5. Which point is in the exterior of ∠AXB? •F •E Answer: Point E, C or D B • C • • •C • X D Questions 12 & 13 Question 5 A 6. If the m ∠DAE = 65 and m∠DAF = 132, find m∠EAF. Answer: 67 B •A •F • D• E 7. Find m∠2 given that m∠1 = 33, m∠3 = 19, and m∠RTV = 105. Answer: 53 U S • • • 2 •R 1 3 T V Question 7 Manchester High School Geometry Midterm REVIEW In the figure l ∣∣ m, and n and p are transversals. m l 10 8. Which type of angles are ∠8 and ∠10? 9 2 1 8 7 5 6 3 4 Answer: Corresponding 9. If m∠7 = 9x +5 and m∠9 = x +37, find the value of x. p Question 54 - 56 Questions 8-9 Questions 46 - 48 9x + 5 = x + 37 8x = 32 x=4 10. What is the m∠7? 113 Given: m∠ 6 = 67 and l ∣∣ m t 1 8 2 7 3 6 4 5 11. Find m∠4. Answer: 67 m l 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? a) m1 = 50, m2 = 130, m3 = 50 b) m1 = 50, m2 = 130, m3 = 130 c) m1 = 130, m2 = 50, m3 = 50 d) m1 = 130, m2 = 50, m3 = 130 6 1 130 5 3 75 2 4 16. What is the measure of ABC? Answer: 79 C A ◀ E ◀ D B F 101 H G n Manchester High School Geometry Midterm REVIEW 17. The circumference of a circle is 84 cm. Find the diameter and the radius. 84∏ = 2∏r C = 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 C = 75.36 cm a. 24 cm. b. 15 in. 12 in. P = 36 in A = 54 sq. in 10 ft. c. All angles are right angles in the figure at the right 2 ft. CHECK 7 ft. A = 109 sq. ft P = 56 feet 9 ft. 16 ft. 20. What is WX? 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 Given : m ∥ n 21. n (2x + 10) What is x? x = 40 m 4 ft. Manchester High School Geometry Midterm REVIEW Write an equation of a line that is parallel to y = 30 = ¾ (16) + b 30 = 12 + b 18 = b New equation y = ¾ x + 18 3 x + 9 and goes through the point (16, 30). 4 1 3 22. Write an equation of a line that is perpendicular to y = x - 10 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. Answer: The rectangle area is 18.75 sq. cm The semicircle is: 2.5 cm 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 12z + 24 = 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 = (5x + 14) + (10x + 16) = 180 15x + 30 = 180 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 The m 3 is The m 4 is The m 5 is 5 65 because: Incoming/Outgoing 65 because: Alternate Interior 65 because : Incoming/Outgoing 25because it completes a triangle 4 3 2 1 Manchester High School Geometry Midterm REVIEW 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) Manchester High School Geometry Midterm REVIEW