SHOW WORK ON ALL FREE RESPONSE. 1. Which of the following is NOT a property of a trapezoid? One pair of parallel sides Diagonals are congruent Length of the midsegment is one-half the sum of the bases Adjacent angles not touching the same base are supplementary 2 points QUESTION 2 1. Find the value of x in the isosceles trapezoid below? x= 4.14 x = 35 x= 21.57 x = 31 2 points QUESTION 3 1. Isosceles trapezoid ABCD has diagonals AC = 10x + 7 and BD = 2x + 41. Find the value of x. x = 11 x=6 x= 4.25 x= 2.83 2 points QUESTION 4 1. If one base angle of an isosceles trapezoid measures 42, what is the measure of the other base angle? 276 222 42 48 2 points 1. QUESTION 5 What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2). Show equations and all work that leads to your answer. 3 points QUESTION 6 1. Find the value of x in the trapezoid below. Show equations and all work that leads to your answer. 3 points QUESTION 7 1. If the length of one base of a trapezoid is 5, the length of the other base is 2x + 7, and the length of the midsegment is 6x - 24, what is the value of x? Show equations and all work that leads to your answer. 3 points Q U E S T I O N 8 -T R A P E Z O I D 1. If the parallel sides of a trapezoid are contained by the lines and , find the equation of the line that contains the midsegment. Show equations and all work that leads to your answer. 3 points 1. Find the value of x in the kite below. TU = 15x - 23 and UV = 3x + 37 x= 4 x= 5 x= 6 x= 7 2 points QUESTION 2 1. Which of the following is NOT a property of a kite? Two pairs of consecutive congruent sides One pair of opposite congruent angles Diagonals bisect each other Diagonals are perpendicular 2 points QUESTION 3 1. TC = 14. What is the length of TV? 7 6 2 8 3 8 2 points QUESTION 4 1. Find the value of x in the kite below. Angle TCU measures (7x - 1) x= 12.7 x = 14 x = 13 x= 14.3 2 points QUESTION 5 1. TV = 20 and CU = 12. Find the length of UV. Show equations and all work that leads to your answer. 3 points QUESTION 6 1. Angle TUW measure (10x - 7) and angle VUW measures (5x + 13). Find the measure of angle TUV. Show equations and all work that leads to your answer. points QUESTION 7 1. Briefly explain, in your own words, the sides that are found in a kite. QUESTION 8-KITE 1. Find the length of TC. TU = 10, UC = 6. Show equations and all work that leads to your answer. 1. EF is the midsegment of trapezoid ABCD. Determine the value of x. 8.2 3.8 5 10. 7 2 points QUESTION 2 1. What is the length of the midsegment AB? 22 31 14. 5 29 2 points 1. QUESTION 3 Which of the following is not a property of an isosceles trapezoid? Each pair of base angles are congruent Congruent diagonals Congruent legs Congruent bases 2 points QUESTION 4 1. WXYZ is a kite, find the measure of WX. 20 28 5.29 10.5 8 2 points QUESTION 5 1. WXYZ is a kite. If the measure of angle WXY is 120, the measure of angle WZY is 4x and the measure of angle ZWX is 10x, find the measure of angle ZYX. 100 171.4 3 40 80 2 points QUESTION 6 1. Quadrilateral ABCD is a kite. Find the measure of angle BCD. 150 68.5 95 190 2 points QUESTION 7 1. Find the perimeter of the kite below, round to the nearest hundredth. 38.8 cm 26 cm 80 cm 19.4 cm 2 points QUESTION 8 1. The area of a kite is 116.25 ft2, one diagonal measures 18.6 ft, find the measure of the other diagonal. 6.25 ft 12.5 ft 3.125 ft 25 ft 2 points QUESTION 9 1. ABCD is a parallelogram; find the area of the shaded region. 120 ft2 60 ft2 90 ft2 150 ft2 2 points 1. Q U E S T I O N 1 0 -T R A P - K I T E The height of a trapezoid is 13 inches, one of the bases measures 22 inches. If the area of the trapezoid is 318.5 square inches, find the length of the other base. 2.5 inches 71 inches 34.25 inches 27 inches 1. The polygon is regular. True Fals e 2 points QUESTION 2 1. Name the polygon by its number of sides. octagon nonagon decagon dodecag on 2 points QUESTION 3 1. The polygon is convex. True Fals e 2 points QUESTION 4 1. Find the sum of the measures of the interior angles of a convex hexagon. 3 points QUESTION 5 1. If the sum of the measures of the interior angles of a convex polygon is 2160, how many sides does the polygon have? 3 points QUESTION 6 1. Exactly four angles of a hexagon are congruent. The other two angles are complementary. What is the measure of one of the four congruent angles? 3 points QUESTION 7 1. Find value of y. 3 points QUESTION 8 1. Find the measure of each interior angle of a regular dodecagon. 3 points QUESTION 9 1. If the measure of each exterior angle of a regular polygon is 9, determine how many sides the polygon has. 3 points 1. QUESTION 10 Find the measure of each exterior angle of a regular 18-gon. 3 points QUESTION 11 1. Find the value of x in the parallelogram below. 102. 3 127 53 106 2 points QUESTION 12 1. ABCD is a parallelogram. Segment AC = 4x + 10. Find the value of x and y. x= 14 x= 7 x= 5 x= 10 1; y = 1; y = 0; y = 0; y = 2 points QUESTION 13 1. MNOP is a parallelogram. If segment PN = 8 and segment AO = 5 find AM 1 6 8 1 0 5 2 points QUESTION 14 1. Which statement is true? All parallelogram are rectangles. All parallelograms are squares All rectangles are parallelograms All rectangles are squares. 2 points QUESTION 15 1. The quadrilateral is a parallelogram. True Fals e 2 points QUESTION 16 1. Given: Complete a 2 column proof. and . Prove: JKLM is a parallelogram. 3 points QUESTION 17 1. Find the perimeter of the parallelogram. 3 points QUESTION 18 1. Find the length of the base of a parallelogram if the area is 380.88 ft 2 and the height measures 13.8 ft. 3 points QUESTION 19 1. Find the area of the parallelogram. 3 points 1. QUESTION 20 Which description would NOT guarantee that the figure was a square? A parallelogram with perpendicular diagonals A quadrilateral with all sides and all angles congruent A quadrilateral with all right angles and all sides congruent. Both a rectangle and a rhombus. QUESTION 21 1. Determine whether parallelogram JKLM with vertices J(-3, -2), K(2, -2), L(5, 2) and M(0, 2) is a rhombus, square, rectangle or all three. 3 points 1. QUESTION 22 Determine if the quadrilateral JKLM with vertices J(3, 3), K(-5, 2), L(-4, -4) and M(4, -3) is a rectangle, using the distance formula. 3 points QUESTION 23 1. Quadrilateral RSTU is a rectangle. If 7x - 10 and 3x + 15, find x. 3 points QUESTION 24 1. Verify that quadrilateral BCDE is a rhombus with vertices B(5, -1), C(-2, 0), D( -1, 7) and E(6, 6) by showing that all four sides are equal. BD = CE = BD = CE = 50 BC = CD = DE = EB = 50 BC = CD = DE = EB = 2 points QUESTION 25 1. Quadrilateral JKLM is a rhombus. The diagonals intersect at N. If the measure of angle KJL is 2x + 5 and angle MJN = 3x - 8 find the measure of angle KLM. 13 62 31 26 2 points QUESTION 26 1. Find the area of a square if the perimeter is equal to 38 in. 3 points QUESTION 27 1. Find the value of x if the area of the rectangle is equal to 136. 3 points QUESTION 28 1. Find the area and perimeter of the rectangle. 3 points QUESTION 29 1. Find the measure of angle WZY if angle YXW is equal to 105. 3 points QUESTION 30 1. Find the value of x. 3 points QUESTION 31 1. Find the value of x and y. 3 points QUESTION 32 1. Find the value of x and y. 3 points QUESTION 33 1. Angle N measures 96 degrees, find the value of x. 3 points QUESTION 34 1. Find the value of x in the kite below. 3 points QUESTION 35 1. Find the area of the trapezoid. 3 points 1. QUESTION 36 If the perimeter of an isosceles trapezoid is 79.53 meters, and the bases measure 25.62 meters and 33.51 meters, find the length of the legs of the trapezoid. 3 points Q U E S T I O N 3 7 - Q UA D A N D P O LY G O N 1. Find the perimeter of the kite below, round to the nearest hundredth. QUESTION 1 1. If angle H = angle R, angle G = angle P, and angle Q = angle F, are the following triangles similar? Justify your answer. 3 points QUESTION 2 1. Your friend is trying to calculate the height of a nearby oak tree. You tell him that you learned how to use similar triangles in Geometry class. You tell your friend to measure his height (75 inches) and you measure the length of his shadow (48 inches). Both of you measure the length of the tree's shadow (38 feet). How tall is the tree (in feet)? Round to the nearest hundredth. 3 points QUESTION 3 1. Are the following triangles similar? Justify your answer. 3 points QUESTION 4 1. Given that ABD is similar to ACE, what is the value of X? Round your answer to the nearest tenth. 3 points QUESTION 5 1. Given the two triangles are similar, what are the values of q and t? Round to the nearest hundredth. 3 points QUESTION 6 1. If , what do you know about the angles? Be specific. 3 points QUESTION 7 1. If , what do you know about the sides? Be specific. 3 points QUESTION 8 1. Are the following triangles similar? Justify your answer. 3 points 1. QUESTION 9 What are the properties of similar triangles? 3 points QUESTION 10-SIMILARITY Given is 4 times smaller than find the length perimeter of and . 1. Explain if . Justify your answer given the following information: HY = 3, YZ = 6, HZ = 7 and YI = 3, IJ = 12, HJ = 14 3 points QUESTION 2 1. Can you prove ? Justify your answer. 3 points QUESTION 3 1. Describe what information would be needed if you wanted to prove Be specific with side lengths, angle names and the postulate that you use. . 3 points QUESTION 4 1. Can you prove that the two triangles are similar? Justify your answer. 3 points 1. QUESTION 5 Are all isosceles triangles similar? Justify your answer. 3 points 1. QUESTION 6 Are all equiangular triangles similar? Justify your answer. 3 points 1. QUESTION 7 Are all equilateral triangles similar? Justify your answer. 3 points QUESTION 8 1. If the dimensions of of , calculate length of are twice as large as the corresponding dimensions and . Then, explain if . 3 points QUESTION 9 1. Is there enough information to prove ?Justify your answer. 3 points Q U E S T I O N 1 0 - P O S T U L AT E 1. Can you prove that the two triangles are similar? Justify your answer. 3 points