Exterior Only this column when the polygon is 1) a) Find the value of x. c) Find the value of x. b) Find the value of x. d) Find the value of x.

Transcription

1 Not a question, write this on the top of your Test Corrections underneath the heading. Sum Each Angle Interior Exterior Only this column when the polygon is 1) a) Find the value of x. c) Find the value of x. b) Find the value of x. d) Find the value of x. c) Find the value of x. e) Find each interior angle of the regular stop sign. 2) Find the measure of an interior angle and an exterior angle of the regular polygon given below: A. Regular hexagon B. Regular dodecagon

2 3) Classify the n-gon by the number of sides for each of the following polygons: a) Each interior angle of the regular n-gon has a measure of 108. b) Each interior angle of the regular n-gon has a measure of 135. c) Each exterior angle of the regular n-gon has a measure of 90. d) Each exterior angle of the regular n-gon has a measure of 60. 4) A regular polygon has an exterior angle measure of (8x+4) and an adjacent interior angle measure of (42x 24). A. Draw a visual to help you see the relationship and solve for x. B. Find the measure of each angle. C. How many sides does this polygon have? 5) Complete the chart. Name pentagon heptagon # Sides 15 Sum of Interior Angles ) a) Determine the smallest degree of rotation that will carry the regular decagon onto itself. Sum of Exterior Angles Each Exterior Angle (if Regular) Each Interior Angle (if Regular) d) Determine all of the degrees of rotation that will carry the regular figure onto itself. 7) Consider the regular octagon below with center at the origin and a vertex at (4,0). Which of the following rotations will map the octagon onto itself. Select all that apply. a) A 45 rotation around the origin. b) A 90 rotation around (4,0). c) A 225 rotation around (0,0). d) A 300 rotation around (4,0). e) A 360 rotation around (0,0). f) A 360 rotation around (4,0).

3 8) Suppose that ABDC is similar to polygon HIJK after a dilation of ABDC. H is at (1,0) and I is at (1,8). Part A: Graph HI on the graph above. What is the scale factor of this dilation? Part B: Find and plot the coordinates of K and J? Part C: What is the relationship (ratio) between the areas of the two polygons? 9) A rectangle has side lengths of 10 and 14. A similar rectangle might have side lengths of: (Draw a visual of each rectangle to test which choice would be similar.) A. 11 and 14 B. 15 and 21 C. 9 and 18 D. 16 and 20 10) You are printing posters for a concert and need them to be 50 tall. The small copy you have is 8 wide by 20 inches tall. Draw a visual. Part A: What scale factor you should use to enlarge the image and make sure the posters are proportional? Part B: How wide will the enlarged poster be? Part C: What relationship (ratio) do the areas of the small copy and the poster have? 11) Overhead Projectors: Your teacher draws a circle on an overhead projector. The projector then displays an enlargement of the circle on the wall. The circle drawn has a radius of 3 inches. The circle on the wall has a diameter of 4 feet. What is the scale factor of the enlargement? (Tip: pay attention to the fact that one is a radius and the other is a diameter make sure you stay consistent). 12) (Hint: draw a visual to help you see the corresponding parts).

4 13) Posters: A poster is enlarged and then the enlargement is reduced as shown in the figure. a) What is the scale factor of the enlargement? the reduction? b) A second poster is reduced directly from size A to size C. What is the scale factor of this reduction? c) How are the scale factors in part (a) related to the scale factor in part (b)? (Hint: how do you get from the scale factors in part a to part b?) 14) Draw a dilation of the figure using the given scale factor. Explain why the two figures are similar. 15) In the diagram, WXYZ ~ MNOP. a) Find the scale factor of WXYZ to MNOP. b) Find the values of x, y, and z. c) Find the perimeter of WXYZ. d) Find the perimeter of MNOP. e) Find the ratio of the perimeter of MNOP to the perimeter of WXYZ.

5 16) Swimming Pool The community park has a rectangular swimming pool enclosed by a rectangular fence for sunbathing. The shape of the pool is similar to the shape of the fence. The pool is 30 feet wide. The fence is 50 feet wide and 100 feet long. a) What is the scale factor of the pool to the fence? b) What is the length of the pool? c) Find the area reserved strictly for sunbathing. 17) Two polygons are similar with a scale factor of 3 to 7. The area of the smaller polygon is 56 in 2. What is the area of the larger polygon? Round to the nearest tenth. 18) The areas of two similar polygons are in the ratio 25: 81. Find the ratio of the corresponding sides. 19) In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table. 20) Quadrilateral HALK is congruent to quadrilateral FORT. m H = 50, m L = 148, and m T = 36. What is m A? 21) Part 1: Use the similarity statement to find the scale factor of the polygon on the left to the polygon on the right. Part 2: Find the perimeter of each polygon (you will need to find each side length first). Part 3: Find the ratio of the perimeters. A) B) 22) Determine if each pair of polygons is similar. If they are, write down the scale factor as smaller to larger. A) B)