b) A ray starts at one point on a line and goes on forever. c) The intersection of 2 planes is one line d) Any four points are collinear.

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1 Name: Review for inal 2016 Period: eometry 22 Note to student: This packet should be used as practice for the eometry 22 final exam. This should not be the only tool that you use to prepare yourself for the exam. You must go through your notes, re-do homework problems, class work problems, formative assessment problems, and questions from your tests and quizzes throughout the year thus far. Section 1 1) lassify each statement as true or false, and explain your reasoning in each false case. a) Two planes intersect in only one point. b) ray starts at one point on a line and goes on forever. c) The intersection of 2 planes is one line d) ny four points are collinear. 2) escribe the difference and similarities of skew and parallel lines. 3) Use the figure below for #6-14. Note that RN pierces the plane at N. It is not coplanar with V. a) Name two segments shown in the figure. b) What is the intersection of M c) Name three collinear points. and RN? d) What are two other ways to name plane V? e) re points R, N, M, and X coplanar? f) Name two rays shown in the figure. g) Name the pair of opposite rays with endpoint N. h) N is the same as N. True or alse? i) NX names a plane. True or alse? 4) onstruct and label the following: a) The circumscribed circle of JKL b) The inscribed circle of MNO K M N O J L

2 5) or the following exercises, do the construction using the figures below. a) onstruct congruent to XY. b) onstruct the perpendicular bisector of XY. c) onstruct a segment parallel to XY. d) onstruct an angle congruent to 2 e) onstruct the angle bisector of X 6) elow each figure write the name of the kind of rigid transformation shown. a. b. c. Section 2 omplete the following statements: 1) and are complementary. m =6x o and m = 12x o. ind x. 2) and are supplementary. m =40x o and m = 20 o. ind x. 3) = 2x + 1, = 16 inches, = 5x 4. Use the diagram to solve for x: 4) Solve for y: m =12y 5, m = 24 o, m = 5y + 6

3 5) WS bisects WV. m WS = 32 o. What is m WV? 6) etermine the value of x: a) b) c) d) 112 o 50 o 2x + 20 x 7) Use the following steps to determine whether the given statement is a definition. a) onditional statement Linear pairs are supplementary, adjacent angles. b) onverse c) iconditional statement d) ecide whether the statement is a definition. xplain your reasoning. 8) Write the conditional statement that corresponds to the Venn diagram below: octor Pediatrician Section 3 1) or the following exercises, refer to the diagram below. Lines m and n are parallel. Name all angles congruent to the given angle and give the theorems or postulates that justify your answer. a) 6 b) 8 c) 5 d) m n 1 2

4 2) or the figure to the right m = 160-3x o, and m H = 35 o. What is x? What Theorem or Postulate supports your answer? H 3) or the figure to the right m = 68 o, and m H = 92-8x o. What value of x makes H? What Theorem or Postulate supports your answer? H 4) ill in the blanks so that the sentences are true. a) The sum of angles in any quadrilateral is. b) In a parallelogram diagonals and opposite angles are c). d) and a have perpendicular diagonals. e) is a quadrilateral with only one pair of parallel sides. f) square is a quadrilateral with congruent sides and right angles. g) rhombus is a with four sides. h) is a quadrilateral with 2 pairs of parallel sides. i) ny four-sided polygon is a. j) rectangle is a quadrilateral with. 5) Polygon is a parallelogram. = 3 in, = 2 in, m = 110 o a) m = c) = b) m = d) =

5 6) MNOP is a rhombus. If m MNO 88, find each of the following: a) m NOP M N b) m OP c) m ON P O 7) Parallelogram RUST m RUS 58 RU 30 cm RQ 9 cm m UST US 28 cm QS m STR ST TQ m TRU TR QU RS UT 50 cm 8) Polygon is a rhombus. = 4x + 2 and = 30. What is x? ive a reason for your equation. 9) Polygon is a rectangle. and intersect to. = 12 ft. What is? 10) Use trapezoid TRP to the right to answer the following: If m T = 60 find the measures of the other angles. m R m m P 11) ind the following. a) NM = b) x = I N 50 M H 32-52x 120 c) What is NM called?

6 12) ind the slope, midpoint, and length of each of the following segments whose endpoints are given. a) (-1, 4) and (4, 10) b) (8, 0) and (10, 6) 13) Lines that are parallel have slopes and lines that are perpendicular have slopes. 14) or the following, a quadrilateral has vertices (2, 5), ( 8, 5), ( 2, 10) and (6, 5). a) raph the quadrilateral on the grid provided. b) What type of quadrilateral is this? Show LL work necessary to justify your answer. Section 4 1) Write a congruency statement for the following polygons. Why are they congruent? H

7 2) etermine whether each pair of triangles can be proven congruent by using the SSS, SS, S or S congruence postulates. If so, identify what postulate is used. a) b) c) 3) etermine whether each pair of triangle scan be proven congruent by using the SSS, SS, S, S or HL congruence postulates. If so, identify what postulate is used and write a congruency statement. a) b) c) Q T P S R U d) N Y e) W X f) R J H M O X Z 4) Label and sate what additional information is required in order to know that the triangles are congruent for the reason given. a) b) c) Y 5) etermine whether or not the triangles below are similar (you may need to do a little work to figure it out) by, SSS, or SS, or none of them. If they are similar, complete the similarity statement. a) b) c) ~ ~ ~

8 d) e) f) LVM ~ TUV ~ WXY ~ 6) etermine whether the polygons are similar, not similar, or not enough information given. If they are similar, determine the scale factor comparing the first to second figure. a) b) 10 c) ) The following polygons are similar; find x and y. a) b) 3 y 5 54 o 2x 1 1 y 8 x x ) N ~ P, = 2 cm., N = 3 cm., = 10 cm., and P = 8 cm. ind N. If m = 36, what is m? 9) Use the following image to explain why the two triangles are similar, then estimate the length of the lake. 10) Solve for x. a) b) c) 5 x x x 12

9 11) Use the diagram to find the height of each building. a) b) c) 16 ft 36 ft 12 ft 24 ft 30 ft 40 ft 20 ft 18 ft 24 ft Section 5 1) or # 1-3 two lengths of the right triangle are given. ind the missing length. a b c a) a = 13 b = c = 14 b) a = 12 b = 16 c = c) a = b = 7 c = 13 2) triangle has side lengths given below. etermine what type of triangle each set is (acute, obtuse, or right Show work to support your answer. a. 24, 40, and 32 b. 30, 24, and 19 c. 6, 14, and 11 3) ind the missing side lengths. Leave your answers in radical form. a) b) c) d) 14 x

10 4) or the following, PQR, m PQR = 90 o, PQ = 6, m QPS = 60 o, and PR = 12. Q a) ind QR = P S R b) ind QS = c) ind SR = d) ind the area of PQR = 5) ind the area of each figure. Round your answers to the nearest tenth. a) b) 4 m 7 ft H 3.5 ft I 6) ind the area of the following figures. a) b) c) 12 ft 8 ft 20 ft 14 ft d) e) f) 7) ind the circumference N area of each figure. Leave your answer in terms of π. a) r = 8 mm b) d = 26 cm c)

11 8) Round your answers to 15a) to the nearest hundredth. = = 9) ind the radius of each circle from the given information. Round to the nearest tenth if necessary. a) rea = 256π in 2 b) ircumference = 120 ft 10) If the area of a parallelogram is 100 cm 2 and the length of the base is 25 cm, what is the height? 11) If the area of a parallelogram is 45 ft 2 and the height is 3 ft, what is the length of the base? 12) If the area of a trapezoid is 250 in 2, the lengths of the bases are 23 in and 27 in, what is the height? 13) If the area of a triangle is 343 u 2 and the height is 14 u, what is the length of the base? 14) ind the area of the shaded region ) ind the area of the composite figures below. km a) b)

12 Section 6 1) or the following, refer to the solid below. a) Name the solid. b) Name a pair of parallel planes. c) Name two segments skew to d) Name two segments to plane. e) What is the volume of the solid if = 4, = 3, and = 2. 2) What is the slant height of a right cone with a radius of 8 in. and a height of 14 in. ind the Surface rea and Volume of each right prism. Round to the hundredth if necessary. 3) ind the Surface rea, Lateral rea, and Volume for the following solids. ive an exact answer. a. b. c. = 12, H = 5, apothem = 6.2 d. e. f. g. h. apothem = 5.2 cm i.

13 j. k. l. m. n. o. 8 cm 6 cm 6 cm 4) The surface area of a square pyramid is given by 540 cm 2 and the side of the square is 10 cm. ind the slant height of the square pyramid. 5) The volume of a cylinder is 960 cubic inches. The height of the cylinder is 15 inches. ind the radius. 6) If a cylinder has surface area of 128 sq ft, and the height of the cylinder is 12 feet, find the radius and the volume. 7) The volume of a spherical ball is 5,000 cm 3. What is the radius of the ball? Section 7 1) ind the degree measures of each arc or angle by using the central angle measures given in M 70 o 84 o 86 o M 34 o a) m c) m e) m g) m M b) m d) m f) m

14 2) etermine arc with length L of a circle with radius 8.5 in and degree measure ) ach polygon circumscribes a circle. What is the perimeter of each polygon? a. b. c. 4) Using circle O below, name the following: a. iameter b. entral ngle c. Minor rc d. Major rc e. Semicircle f. Radius g. Tangent h. Point of Tangency H O K L 5) or the following, in M, is the diameter, is tangent to the circle at point, and m = 78 o. a) m b) m M c) m d) m e) m f) m g) is a minor arc, is a major arc h) is a radius, is a. i) is a In M, if = 12, = 16, and =20, find the following: j) = k) =

15 15) What is the value of x? Lines that appear to be tangent are tangent. Round to the nearest hundredth if necessary. a) b) c) d) 16) Write the equation for the circle with center (2, 4) and radius = 7 in 17) Write the equation for the circle with center (-3, 1) and diameter = 18 in 18) ind the center and radius of the circle: 2 2 ( x 7) ( y 12) ) ind the center and radius of the circle: (x + 5) 2 + (y + 8) 2 = ) raph the circle on the coordinate plane. a. 2 2 ( x 2) ( y 4) 16 b. 2 2 ( x 7) ( y 8) 1 c. 2 2 ( x 2) ( y 3) 36

16 Section 8 1) Using the triangles below, determine the trigonometric ratio. Leave your answers as simplified fractions. a) tan = b) cos = c) sin = d) tan = H 2 2) ind the marked side of each of the following triangles. a) b) c) d) 3) ind the value for each of the marked angles. a) b) c) d) 4) skateboarding ramp is 12 in. high and rises at an angle of 17. How long is the base of the ramp? What is the length of the ramp? Round your answer to the nearest inch. 5) Joey is walking home from the library. He can walk for 1 mile along the street, then turn right and walk 1.5 miles along another street; or he can cut across a large field straight to his house. t what angle,, should he head off from the library, and how far, d, should he cut across the field? = 1.5 m H d = 1 m d L

17 Proofs 1) iven: and are right angles, Prove: Statements Reasons 1. and are right angles, and are right triangles ) ill in the blanks in the table below to prove Statement Reason & are vertical angles

18 3) iven: m 1 100, m 2 80 Prove: l m Statements Reasons 1. m 1 100, m iven 2. 2 and 3 form a linear pair and 3 are supplementary 3. Linear Pair Property 4. m 2 m m m m 1 m and 3 are orresponding ngles l m 10. 4) iven: O ; m 38 Prove: m 71 o o Statements Reasons 1. O 1. iven 2. O m m O m 38 o m m m O 180 o m 38 m 180 o m o m 142 o