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 1. using the Angle-Angle Similarity Postulate. True Fals e 2 points QUESTION 2 1. The Angle-Angle Similarity Postulate states that \"If two angles of one triangle are congruent to 2 angles of another triangle, then the triangles are congruent\" True Fals e 2 points QUESTION 3 1. Complete the reason for step 4 in the proof below: Given: Prove: Step Statements Reasons 1 Given 2 Alternate Interior angles 3 Alternate Interior angles 4 Side-Angle-Angle Similarity Postulate Side-Side-Side Similarity Postulate Angle-Angle-Angle Similarity Postulate Angle-Angle Similarity Postulate 2 points QUESTION 4 1. Given the triangles are similar, calculate the values of m and n. Round to the nearest tenth n= 7.5 n= =7 n= 3.5 n= =3 3, m = 7.5, m 3, m = 7.5, m 2 points QUESTION 5 1. Determine whether the pair of figures are similar and explain why. The two triangles side lengths The two triangles angle measures The two triangles proportional The two triangles are not similar because they have different are not similar because they have different are similar because their angles are are similar because their sides are proportional 2 points QUESTION 6 1. Find the measure of x and y. x = 18, y = 13 x = 62, y = 30 x = 7, y = 30 x = 7, y = 3 2 points QUESTION 7 1. Given 1 5 1 2 1 3 1 6 and BC = 8, what is the value of EF? 2 points QUESTION 8 1. At a certain time of day, a 5 foot tall man has a 7.5 foot shadow. If a tree is 20 feet tall, what is the length of the shadow of the tree? 30 feet 12 feet 24 feet 15 feet 2 points QUESTION 9 1. ABC is similar to DEF. To one decimal place calculate the value of x 52 8 8.4 10. 4 2 points QUESTION 10 1. The Side-Angle-Side Similarity Postulate states \"If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are congruent\"? True Fals e 2 points QUESTION 11- SIMILAR TRIANGLE 1. Use the Side-Splitter Theorem to find x, given that . The figure is not drawn to scale. 6 1 2 2 0 2 4 1. Describe in your own words, what it means if two polygons are similar. 3 points QUESTION 2 1. The figures below are similar; illustrate what you know about the angles. 3 points QUESTION 3 1. The figures below are similar; explain what you know about the sides. 3 points 1. QUESTION 4 Tory has two similar picture frames in her bathroom. The ratio of the larger picture frame to the smaller picture frame is 5:2. If the perimeter of the smaller picture frame is 30 in, what is the perimeter of the bigger picture frame? 3 points 1. QUESTION 5 As the marketing designer for Burger King, you are given a 4 in by 6 in logo and have been told to create an advertisement with sides six times larger. What is the area of your advertisement (in feet)? [12 inches = 1 ft] 3 points QUESTION 6 1. Bryan is an art sculptor and is creating an art series made entirely of similar figures. He buys a Sponge Bob Square Pants figure and decides he wants to make a larger version that has sides 15 times bigger. If the area of the figure is 12.5 cm 2, what is the area of his sculpture? 3 points QUESTION 7 1. Calculate the value of OK. 3 points QUESTION 8 1. Find the value of y in the similar figures below. 3 points QUESTION 9 1. Given the figures are similar, calculate the perimeter of the ABCDE. 3 points 1. 1. Q U E S T I O N 1 0 - S I M I L A R P O LY. D E F Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the smaller roof is 4.5 feet, find the corresponding altitude of the larger roof. Round to the nearest hundredth. If then AB = EH, BC = HF, CD = FG, AD = EF True Fals e 2 points QUESTION 2 1. If then True Fals e 2 points QUESTION 3 1. Given calculate the value of WE, BR, and EQ WE = 5, BR = 11.25, EQ = 7 WE = 11.25, BR = 5, EQ = 7 WE = 5, BR = 7, EQ = 11.25 WE = 7, BR = 11.25, EQ = 5 2 points QUESTION 4 1. Find the value of x in the similar figures (round to the nearest tenth) 12 6 13. 3 7.3 2 points 1. QUESTION 5 A regular pentagon has side length 12 cm. The perimeter of the pentagon is 60 cm and the area is 247.7 cm2. A second pentagon has side lengths equal to 24 cm. Find the perimeter of the second pentagon. 329 cm 144 cm 150 cm 120 cm 2 points QUESTION 6 1. Given what is the perimeter of BRAIN? 23.50 58.7 5 35.2 5 57.2 5 2 points QUESTION 7 1. A regular octagon has side length 10.9 in. The perimeter of the octagon is 87.2 in and the area is 573.67 in2. A second octagon has side lengths equal to 21.8 in. Find the area of the second octagon. Round to the nearest hundredth. 261.60 in2 2294.68 in2 317.06 in2 142.66 in2 2 points 1. QUESTION 8 You have been asked to create a sign for Sonic and have been given a 4 in by 6 in logo to enlarge. Your boss told you to make sure the ratio of the logo to the billboard was 2 inches:15 inches. What are the dimensions of the logo on the billboard? 35 in by 40 in 35 in by 45 in 30 in by 40 in 30 in by 45 in 2 points QUESTION 9 1. Becky is growing a garden in her backyard. It is in the shape of a rectangle 3 feet wide by 4 feet long. Her husband said that he can grow the same amount of crop in half of the space. What are the dimensions of his garden? 8 feet by 6 feet 1.5 feet by 2 feet 6 feet by 8 feet 2 feet by 1.5 feet 2 points 1. Q U E S T I O N 1 0 - S I M I L A R P O LY G O N The Johnson's have a square rug in their living room that is 36 ft2. For Christmas, they are building a dollhouse for their daughter. Its linear dimensions are exactly 60 times smaller than their actual house. In the dollhouse, what are the dimensions of the rug (in inches)? [12 inches in 1 foot] 12 inches by 12 inches 7.2 inches by 7.2 inches 0.1 inches by 0.1 inches 1.2 inches by 1.2 inches