Geometry Review (1 st semester)

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1 NAME HOUR Geometry Review (1 st semester) 1) The midpoint of XY is Z. If XY = n and XZ = n + 15, what is YZ? A) 18 B) 6 C) 45 D) 90 ) What is RS? A) 5 B) 56 C) D) 70 ) Which is an obtuse angle? A) PQR B) R C) PSQ D) P 4) Which is the measure of a straight angle? A) 0 B) 90 C) 100 D) 180 5) Which angle is supplementary to RLK? A) RLQ B) RLP C) RLM D) PLM 6) What is m 1? A) 76 B) 104 C) 108 D) 156 7) The measures of two supplementary angles are (x 10) and (6x + 100). What is the measure of the smaller angle? A) 0 B) 0 C) 10 D) 6.67

2 8) The area of a square is 16 cm². What is the perimeter? A) 4 cm B) 8 cm C) 16 cm D) cm 9) To the nearest whole number, what is the circumference of a circle whose radius is 1.5 ft? C = π r A) 0 ft B) 79 ft C) 9 ft D) 491 ft 10) To the nearest tenth, what is the distance between (7, -4) and (-, -1)? A) 5 B) 10.4 C) 0.5 D) ) Find the next item in the pattern:, 8, 18,, 50, 7,... A) 74 B) 76 C) 94 D) 98 1) Which is a counterexample that disproves the conjecture If the area of a rectangle is 6 square units, then the perimeter is less than 6 units? A) a 6 by 6 rectangle B) a 4 by 9 rectangle C) a by 1 rectangle D) a by 18 rectangle 1) Which conditional statement is true? A) If it is raining outside, then the ground is wet. B) If a person lives in the United States, then the person lives in Chicago. C) If a number is divisible by, then the number is odd. D) If today is Saturday, then yesterday was Sunday. 14) What is the inverse of the statement If the key fits, then the lock opens? A) If the lock opens, then the key fits. B) If the key does not fit, then the lock does not open. C) If the lock does not open, then the key does not fit. D) If the key fits, then the lock does not open.

3 15) For which statement is the converse false? A) If Mary can swim, then she can swim the crawl. B) If it is raining outside, then the temperature is above freezing. C) If Greg has two children, then he has one son and one daughter. D) If Carolyn can stand up, then she can walk. 16) What is the contrapositive of the statement If a triangle has at least two congruent angles, then it is an isosceles triangle? A) If a triangle has no congruent angles, then it is not an isosceles triangle. B) If a triangle is an isosceles triangle, then it has at least two congruent angles. C) If a triangle does not have at least two congruent angles, then it is an isosceles triangle. D) If a triangle is not an isosceles triangle, then it does not have at least two congruent angles. 17) Which is a counterexample of the statement If an animal has wings, then it can fly? A) penguin B) duck C) robin D) rabbit 18) Given: If Maria passes geometry, then she will graduate. Maria passes geometry. What can you conclude? A) Maria will take geometry. B) If Maria does not graduate, then she is not taking geometry. C) If Maria does not take geometry, then she will graduate. D) Maria will graduate. 19) Given: If all four angles of a parallelogram are right angles, then the parallelogram is a rectangle. If a parallelogram has at least one right angle, then all four angles are right. Which conjecture is valid? A) If a rectangle has four right angles, then the rectangle is a parallelogram. B) If a parallelogram has at least one right angle, then the parallelogram is a rectangle. C) If all four angles of a parallelogram are right angles, then at least one angle is a right angle. D) If a parallelogram is a rectangle, then the parallelogram has at least one right angle.

4 0) Which is a biconditional statement for the given conditional? If two coplanar lines do not intersect, then they are parallel. A) Two coplanar lines intersect if and only if they are not parallel. B) Two coplanar lines do not intersect if and only if they are parallel. C) Two coplanar lines are not parallel if and only if they intersect. D) Two coplanar lines intersect if and only if they are parallel. 1) Which biconditional statement is true? A) Peter lives in Cincinnati if and only if he lives in Ohio. B) A rectangle has sides and 5 if and only if its area is 15. C) Two segments are congruent if and only if they have the same measure. D) Two angles measure 90 if and only if they are supplementary. ) What is missing from the proof? Given: m 1 = m, m 1 = 90 Prove: is a right angle. Proof: A) Definition of congruence B) Definition of perpendicular C) Definition of right angle D) 1 is a right angle. Refer to the figure for Exercises and 4. ) Which pair of angles are corresponding angles? A) 1 & B) 1 & 4 C) 1 & D) 1 & 6 4) Which completes the statement Angles 6 and 7 are an example of angles? A) same-side interior B) alternate interior C) alternate exterior D) corresponding

5 5) Which angle is the alternate interior angle with 4? A) 1 B) 7 C) 5 D) 8 6) If lines p and q are parallel, what is the value of x? A) 15 B) 45 C) 0 D) 90 7) If j k, which could be one of the angle measures? A) 5 B) 7 C) 60 D) 84 8) If u v, what is the value of y? A) 58 B) 14 C) 1 D) 155 9) If r s, what is the value of y? A) 18 B) 60 C) 10 D) 16 0) Which angle must be congruent to 8 to prove that u v? A) 1 B) C) D) 4 1) Which information CANNOT be used to prove that j k? A) 7 B) 7 is supplementary to 6 C) 1 5 D) 1 is supplementary to

6 ) Which completes the statement The floor and ceiling of a room represent planes that are? A) skew B) intersecting but not perpendicular C) perpendicular D) parallel ) Which inequality must be true, given the information in the figure? A) x < B) - > x C) x > D) x < - 4) What is the slope of a line that passes through the points (,) and (7,-1)? A) 7 B) 1 C) D) 1 7 5) What is the slope of the line whose equation is x 6y = 0? A) 1 1 B) C) D) 6) Which is an equation of the line in the graph? A) y = x B) y = x + C) y = x + D) y = x + 7) A given line has a slope of 8. What is the slope of a line that s parallel to it? A) B) 8 8 C) 8 D) 8 8) What is the equation of the line that passes through (-8, 8) and has a slope of? A) y = 8x B) y = 8x + C) y = x + D) y = x + 16

7 9) The graph of which line is perpendicular to the graph of y = x + 1? A) y = x + 1 B) y = x + 6 C) y = ½x + 1 D) y = ½x ) The measures of two angles of a triangle are 18 and 6. Which type of triangle is it? A) acute B) obtuse C) equiangular D) right 41) Which best describes the triangle? A) acute isosceles B) acute scalene C) right isosceles D) right scalene 4) What is m A? A) 1 B) 6 C) 48 D) 50 4) If PQR STU, which angle is congruent to U? A) P B) R C) Q D) S 44) Which information would you need so that MNP UVW by ASA? A) P W B) MN UV C) MP UW D) NP VW

8 45) What would allow you to prove QRS XYZ by HL? A) QS XZ B) R Y C) Q X D) Q and X are right angles 46) Given the figure, why is BC QR? A) SAS B) AAS C) ASA D) CPCTC 47) QS bisects PQR. What is QR? A) 65 B) 40 C) 50 D) 15 48) XL, XM, and XN are perpendicular bisectors. The perimeter of FGH is 54. What is FG? A) 6 B) 18 C) 7 D) 9 49) What are all possible values for x? A) x < 8 B) x > -1 C) x > 8 D) -1 < x < 8 50) Which equation represents the perpendicular bisector of the segment whose endpoints are (0, 6) and (8, 10)? A) y = x 6 B) y = ½x + 4 C) y = x + 10 D) y = ½x + 14

9 51) What is the measure of TWX? A) B) 4 C) 44 D) 84 5) Which list shows the angles in order from greatest measure to least measure? A) X, Y, Z B) Y, X, Z C) X, Z, Y D) Y, Z, X 5) A triangle with side lengths 1, 0, and 0 can be classified as. A) acute B) right C) obtuse D) equiangular 54) Use special right triangles to solve for x in this equilateral triangle. A) 4 B) 8 C) 16 D) 16 8 X 55) Use special right triangles to solve for x. A) 4 B) 1 X C) 6 D)

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