FINAL REVIEW. 1) Always, Sometimes, or Never. If you answer sometimes, give an example for when it is true and an example for when it is not true.

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1 FINL RVIW 1) lways, Sometimes, or Never. If you answer sometimes, give an eample for when it is true and an eample for when it is not true. a) rhombus is a square. b) square is a parallelogram. c) oth pairs of opposite sides of a trapezoid are parallel. d) The diagonals bisect the angles of a parallelogram. e) rhombus is a rectangle. f) The diagonals of a kite bisect each other. g) The legs of a trapezoid are congruent. h) If FGIJ is an isosceles trapezoid, then < F is supplementary to < I. i) If the diagonals of a parallelogram are congruent, it is a square. j) The diagonals of a parallelogram are perpendicular. k) If one angle of a parallelogram is right, the parallelogram is a rectangle. l) The diagonals of a trapezoid bisect each other. 2) is a parallelogram. = and =. Solve for and the length of 3 3) Give the most descriptive name that you can for each quadrilateral: 4) In parallelogram MTH, if <M = 145, then <= 5) Quadrilateral has coordinates (1,4), (4,9), ( 1,12), ( 4,7). What is the most descriptive name for? Justify your response with words and math!!! 1

2 6) a. Graph the vertices of quadrilateral : (0, 6), ( 4,2), (4,6) and (8, 2). b. Find the slopes of,,, and. c. What is the most descriptive name for quad? d. Find the slopes of and. e. Now, what is the most descriptive name for quad? f. (t this point, you should have enough information to know that quad is a square.) Verify that all sides of square are equal by finding the lengths of,,, and. 7) Given: Parallelogram = 10!y = 8 + 2y +14 = 7 + 4y +23 = 3!2y + 3 " = (10!12y!10)! a) Solve for and y. b) What are the lengths of,,,? c) What is the measure of "? d) What is the most descriptive name for parallelogram? 8) is a parallelogram < = ( 3 + 5)! < = ( )! Find the measure of <. 9) is a parallelogram = 4! y = 2 + y = 6 = 6 Solve for and y. 2

3 10) QU is a parallelogram. Give the most descriptive name for QU. UF = 2 y, F = 18, QF = +y, F = 6+2y, "QF = (10)! U F ( 10) Q 11) is a parallelogram = 4 = + y = 2y = 3! 7 Solve for and y. 12) In parallelogram, < is three times as large as <. Find <. 13) If two of the angles of a parallelogram are in the ratio 2:1, what are the four angles? 14) Name the most specific quadrilateral that you can based on the marks on the diagrams Z Y W X Z Y W X 3

4 15) Fill in the blanks: a) The definition of an isosceles triangle specifies that two be congruent. b) quadrilateral with eactly one pair of parallel sides is a. c) The diagonals of a quadrilateral are congruent and they are perpendicular bisectors of each other. The quadrilateral can best be described as a. d) The verte angle of an isosceles triangle is 50!. ach base angle is degrees. e) parallelogram with congruent diagonals must be a. f) quadrilateral with four congruent sides may be a, but must be a. g) The diagonals of a quadrilateral are not congruent, but they bisect each other. The quadrilateral must be a, but it cannot be a. 16) Solve for : 17) Given: #GHI ~ #XYZ m"g = 3 + 4, 166 m"x = 2y + 3, Find: m"y m"y = 4y , m"i = 2y ) What value of makes similar to? ) Solve for : 20) Name the triangles that are similar and solve for and y: 9 4 y

5 21) The sides of a triangle are 5, 9, and 10. similar triangle has a perimeter of 60. Find each side of the second triangle. 22) Solve for : 23) Given: # ~ #F = +4 F = = +2 F = a) Solve for. b) Find the length of. c) What are the restrictions on? 24) Solve for : 25) Find the tan" ) sin" = 5. Solve for. 27) Find the lengths of PM and MT. 9 4 P 5 3 S 6 3 M T 28) sin < = 5 6 a) Find the length of. b) Find the length of. c) Find cos <. d) Find tan < ) valuate each of the following... your answer must include a justification. a) cos60! b) tan60! c) sin45! 30) If = an acute angle and tan=1, then the measure of is? 31) Rhombus has =12 and m<=60, find and. 5

6 32) Find the altitude of an isosceles triangle whose base is 14 and whose perimeter is ) Solve for for the following trapezoid: ) The radius of a circle inscribed in a square with a perimeter of 20 feet is: 35) The radii of two concentric circles are 3 and 21. Find the length of the chord of the larger circle that is tangent to the smaller circle. 9 36) PSRQ is an inscribed quadrilateral. PSR = 97!. Find the measure of "S. P S R Q 37) In circle Q, " SQR = 48 and RQ = 70 cm. 38) TX is tangent to circle Y at point Z. Find the LNGTH of minor arc SR. If XY = 41 and XZ = 9. Find PX. S Y Q R P X T Z 39) How far from the center of a circle with radius 50 is a chord of length 80? 40) In circle, " LT = 60º. If L = 15, find the length of the chord TH. T L H 41) O is the center of the circle. rc = 70! and rc = 40!. < = 35!. Find all arcs and angles that you can! 70 O

7 42) UY is tangent to circle S. 43) Find arc. Find the area of the circle if SU is 41 and YU is 40. lso find ZU. U Z 4 S Y 3 44) The radii of two concentric circles are 9 and 15. Find the length of the chord of the larger circle that is tangent to the smaller circle. 45) and are chords of a circle intersecting at X, and X is the midpoint of. If X = 8 and X = 18, find the length of. 46) Solve for and y. 47) Two concentric circles have radii 10 and 16. Find the length of a chord of the larger circle that is tangent to the smaller circle. y 53 48) The radius of circle O is 7. Find: a. measure of arc b. measure of arc c. m< d. m< e. the perimeter of # f. the length of altitude g. the perimeter of # 60 O 49) is a quadrilateral inscribed in a circle. If arc = 70, arc = 110, and arc = 90, find the size of each angle of the quadrilateral. 50) If the point (2,3) is the center of a circle and the circle passes through the point ( 6, 8), what is the diameter of the circle? 51) Find the length of the arc of a sector with a 40 central angle in a circle of radius of ) Find the area of the sector of a circle with a 40 central angle in a circle of radius of ) The bases of a trapezoid are 8 feet and 15 feet. The area of the trapezoid is 115 square feet. The height of the trapezoid is: 7

8 54) regular heagon whose perimeter is 300 is inscribed in a circle. Find the area between the circle and the heagon. 55) The legs of a right triangle are 16 and 20. Find the length of the radius of the circle that circumscribes the triangle. 56) triangle has sides 8, 8 and 12. Find the area. 57) Find the area of an equilateral triangle with a side of ) rhombus has sides of length 10 and one of its angles has a measure of 60!. Find the area of the rhombus. 59) In parallelogram, if = 15, = 8, and angle = 30, find the area of. 60) In isosceles triangle with = = 10, and angle = 45, find the area. 61) n isosceles trapezoid has bases of 18 and 28. Its area is 96. Find its altitude. 62) Find the radius of a circle inscribed in (a) a square with perimeter of 20 (b) an equilateral triangle with perimeter of 18 (c) a regular heagon with a perimeter of 60 63) rhombus has diagonals of 20 and 30. Find its area. 64) n isosceles trapezoid has bases of 8 and 10, with base angles of 60. Find the area. 65) Find the R of the figure shown ) Find the area of an equilateral triangle with a side length of 9. 67) The area of a square is 11u 2. The length of the diagonal of the square is: 68) square is inscribed in a circle. If the radius of the circle is 6 3, find the area of the square. 69) Find the area of the rectangle formed by the the lines y =!9, y = 14, = 8, = ) Find the area of an isosceles triangle if the legs are 20 and the base is 30. 8

9 71) P is the center of the circle. Find the area of the shaded region P 72) Verify that is a parallelogram and find the area and perimeter of. (4, 9), (9, 9), (3, 3), and ( 2, 3). 73) Find the area and perimeter of #. (1, 2), (1, 6), and (4, 1) 74) Find the area and the perimeter of 75) regular heagon with side of trapezoid. length 14 is inscribed in a circle. Find the area of the shaded region ) # has coordinates ( 10, 1), (7, 1), (10, 5). Find the area and the perimeter of #. 77) circle is inscribed in an equilateral triangle with side length 8 6. Find the area of the shaded region. 78) This cone has a height of 15 cm and a radius of 5 cm. Find its volume. 79) Two spheres have radii 4 and 14. What is the ratio of their volumes? 80) Find the areas and volumes of each. Please break surface area down into lateral area and area of the base(s) : (a) sphere with radius of 4 (b) cylinder with base diameter of 12 and height of 10 (c) cone with base radius of 3 and an altitude of 4. (d) prism whose bases are equilateral triangles with sides of 8, and whose height is 12 (e) cube whose faces have diagonals of 9. (f) heagonal prism whose bases have a perimeter of 36 and whose height is 10. 9

10 81) Two spheres have radii of 2 and 4. What is the ratio of their volumes? What is the ratio of their surface areas? 82) Find the total surface area of the rectangular prism: 83) Find the volume of the figure which is made up of a 6 in 12 cylinder with a half sphere on top. 16 in 8 in 3 in 84) Find the TOTL SURF R of a cylinder with radius of 4 and height of ) square base pyramid has a slant height of 17 cm and a height of 15 cm. Find the volume of the pyramid ) prism has right triangle bases with legs 7 and 24. The height of the prism is 9. Find the total area of the prism. 87) regular square pyramid has a slant height of 12 cm and a height of 8 cm. Find the area and volume. 88) hemisphere sits on top of a cylinder whose diameter is 8 and whose height is 12. Find the volume and the surface area of the entire figure. 89) The area of a trapezoid is 72 and its altitude is 6. Find the lengths of the bases if one is twice as long as the other. 90) Find the area of a circle whose circumference is 20π. 91) triangle has vertices (1, 8), ( 3, 7), and ( 9, 12). a) Find the equation of the perpendicular bisector of. b) Find the equation of the line parallel to that passes through. c) Find the equation of the altitude from. d) Find the equation of the median from. 92) Find the perimeter and the area of an equilateral triangle with a height of 9. 93) Given two points ( 4, 3) and (6, 5), find the equation of the perpendicular bisector of segment. 94) Given the equation 3 (y + 4) 2 = y a) Find the slope of this line b) Find the slope of any line perpendicular to this line c) Find the slope of any line parallel to this line d) Find the and y-intercepts of this line 10

11 95) What is the equation of the line in y = m + b form with a slope of 2/3 that passes through the point (4, 2)? 96) On a piece of graph paper, sketch each equation: a) y = 1! 3 b) y = 3 c) 2y + 3 = d) y = 2 97) What is the equation of the line that is parallel to the -ais and passes through the point (10,-17)? 98) What is the equation of the line that is perpendicular to the -ais and passes through the point (-7, 10)? 99) What is the equation of the line (in point-slope form) that passes through the points (5,1) and (23,-12)? What is the equation of the same line in slope-intercept form? 100) What is the equation of the line (in slope-intercept form) that has a slope of 4 3 and passes through the origin? 101) What is the equation of the line (in slope-intercept form) that passes through the points (0, 5 2 ) and (! 7 3, 0) 102) The coordinates of are (-3,8) and the coordinates of are (7,-4). $ &% a) Find the equation of the line that is parallel to and passes through the point (1, 2). $ &% b) Find the equation of the line that is perpendicular to and passes through the point ( 5, 6). 11