Pre-AP Geometry. True or False: 1. Points A, B, and D are collinear. 2. Points B, F, and H are coplanar. 3. Points H, B, D, and A are coplanar.

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1 Pre-AP Geometry Unit 1 Test Review Name: Date: Period: True or False: 1. Points A, B, and D are collinear. 2. Points B, F, and H are coplanar.. Points H, B, D, and A are coplanar. 4. XV is the same as XY 5. WX is the same as XW 6. ZX is the same as WZ 7. YX is the same as YV 8. XV and XY are opposite rays. 9. Find AC. 10. Find CD. A B C D Solve. Show work. K L M 11. L is the midpoint of KM 12. KL = 2x + 9, LM = x + 4, KM = 8x - 20 KL = x 8 LM = x + 10 x = KL = x = KM = 1

2 BE bisects DBC. Find the value of x. 1. m = 6x, m DBC = 90 - x D E 2 1 C B A 14. m 1 = 7x +, m 2 = 6x m 1 = x, m = 4x True or false. 16. ACB and ECA form a linear pair. 17. C is the midpoint of AD 18. AC = AD B A C D 19. ECA BCA 20. BC AD 21. C is the midpoint of BE E 22. The measure of an angle is 11 9 as large as its complement. Find the measure of the angle and of the complement. 2. A supplement of an angle is 11 times as large as a complement of the angle. Find the measure of the angle, its supplement, and its complement. 2

3 Find x. Show work x - 21 x Find the distance from A to B and the coordinates of the midpoint of AB. Show work. 27. A(-2, -1) B(-4, ) 28. A(12, -1) B(0, -6) 29) AB is a diameter is the given circle. If A(-4, -5) and B(2, -1), find the center of the circle and the length of the radius. A C B C(, ) radius

4 Find each answer. 0. The coordinates of the midpoint of ST 1. The midpoint of EF is (-, 7). are (-, 5). The coordinates of S are The coordinates of E are (-, 10). Find (8, 1). Find the coordinates of T. the coordinates of F. Complete each statement with always, sometimes, or never to make a true statement. 2. Two points are collinear.. Three planes intersect in exactly one point. 4. If two planes intersect, then they intersect in exactly one line. 5. Two lines intersect in more than one point. 6. Three points are coplanar. Solve each: 2 11x 7) = 5x 7 2 8) ( x 5) = x 2x 6 Simplify each: 9) (2x y 4 ) (x 5 y) 2 40) x x 5 y y 2 41) (x 8) 2 4

5 42) The pattern of squares below continues infinitely, with more squares being added at each step. First Step Second Step Third Step Which expression can be used to determine the number of squares in the nth step? A 2n B n(n+2) C n(n + 1) D 2(n+ 1) E n + Solve. Show work. 4) Complete the table below. Then use the information in the table to answer the question below. The first 2 numbers of a sequence are 1 and, respectively. The third number is 4, and, in general, every number after the second is the sum of the two numbers immediately preceding it. How many of the first 1,000 numbers in this sequence are odd? A B 500 C 665 D 666 E 667 Pattern Table Number of Term Number 1 st Term 2 nd Term rd Term 4 th Term 5 th Term 6 th Term 7 th Term 8 th Term 9 th Term 44) Write the converse, inverse, and contrapositive for the following conditional statement. Label each statement including the conditional as true or false. Conditional: If x = -6, then x = 6 Converse: Inverse: Contrapositive: 5

6 . 45) 46) Decide if the following statement is true or false. If it is false, give a counterexample. Qqqqqqqqqqqqqqqqqq If xy 0, then x 0. 47) An athletic field is a rectangle, 100 yards by 40 yards, With a semicircle at each of the short sides. A running track 10 yards wide surrounds the field. Find the perimeter of the outside of the running track to the nearest tenth of a yard. 48) The base of a rectangle is 5 feet less than six times the height of the rectangle. The area of the rectangle is 56 square feet. Find the base and height of the rectangle. Show algebraic work. 6

7 Study assignments from these two chapters that deal with problem solving. Be sure you can do the four constructions. Solutions Review Chapter 1 PAP 1) F 2) T ) F 4) F 5) T 6) T 7) T 8) T 9) 7 10) 2 11) x = 9 KL = 19 12) x = 11 KM = 68 1) 18 14) 4 15) 0 16) T 17) F 18) F 19) T 20) T 21) T 22) comp is 49.5 and angle is )angle is 81, supp is99, comp is 9 24) 9 25) 15 26) ) 2 5 (-, 1) 28) 1 (6, -.5) 29) center is (-1, -), radius = 1 0) (-14, 9) 1) (-,4) 2) Always ) Sometimes 4) Always 5) Never 6) Always 7) 2 1 8) 8 5 or ) 72x 19 y 14 40) x 2 y 41) 9x 2 48x ) D 4) E 44) Conditional True; Converse: If x = 6, then x = -6 False 45) A Inverse: If x -6, then x 6 False Contrapositive: If x 6, then x -6 True 46) One example is x = 4 and y = -2; This isn t the only example. To check your example, be sure x is a positive number and y is a negative number and neither should be zero. 47) 88.4 yds 8 48) The two solutions to the equation are x =.5 and x =. The only geometric solution is x =.5 since the height can t be a negative number. The height is.5 feet and the base is 16 feet. 7