Geometry 2 nd Semester Review Packet PART 1: Chapter 4

Transcription

1 Geometry 2 nd Semester Review Packet PART 1: Chapter 4 Name 1. Determine if these are scale figures. If so state the scale factor, treating the larger image as the original figure, and the smaller as the new figure. Fill in all missing angles. If not, change sides to make it a scale figure, and then state the scale factor The following are scale figures. State the scale factor, treating the left figure as the original. Then find the value of x. 8 4 x 10 y For a given triangle, describe the effects of a scale factor on the area and perimeter. Can you predict the area and perimeter of a scaled copy without scaling the original triangle?

2 4. The two figures below are scale figures. Fill in the missing sides and angles. Round to the nearest hundredths, if necessary You scale a polygon by the factor 2. You then compare the original polygon to the scaled polygon. Find the ratio of 5 each pair of measurements. a. Any two corresponding sides of the polygons b. Any two corresponding angles of the polygons c. The perimeters of the two polygons. d. The areas of the two polygons.

3 6. Given: ABC DEF AB = 60 BC = 56 DE = 144 DF = m A = 64 m E = 50 a. Find m B. b. Find m C. c. Find m D. d. Find m F. e. Find AC. f. Find EF. 7. ΔQRS ΔTUV, QR = 12, RS = 34, UV = 115.6, and TV = 220. Find the perimeter of TUV. Show your calculations. 8. Place a point of dilation inside the rectangle given. Now scale the rectangle by a factor of 3 using the ratio method. Be clear in how you are doing it, so that I know that you are using the correct method.

4 9. Using the parallel method, scale the following by a factor of 1/2 using the given point of dilation. Be clear on how you are doing it, so that I know you are using the parallel method. 10. Find x and y. Show all your work. (The diagram is not drawn to scale!!!) 6 x y 11. You are looking up at a statue that is 5 feet away from you. When you look at the top of the statue, you notice that the top of the statue lines up perfectly with the top of a building. You know the height of the building is 500 feet and the height of the statue is 10 feet. How far away is the statue from the building? Make sure you draw a picture of the situation for full credit.

5 12. Find x and y. Show all your work. (The diagram is not drawn to scale!!!) 22 x y 13. Find x and y. Show your calculations. x y

6 15. In the figure at the right, AB = 12, BC = 6, AC = 9, DC = 2, and EC = 3. Prove that ABC ~ EDC. 16. Using a paragraph or a proof, and the three triangle similarity shortcuts, prove the following: F Given: FD FG 1 2 Prove: ADE HGE 2 H A D E G 17. GHIJK is a heptagon with an area of 29 square centimeters and a perimeter of 15 centimeters. GHIJK is scaled by a factor of 5 to produce LMNOP. a) Find the area of LMNOP. Show your calculations and include units. b) Find the perimeter of LMNOP. Show your calculations and include units.

7 18. Given: AC = 60 BC = 100 CE = 125 DC = 75 Are the two triangles similar? Justify your answer. If the triangles are similar, your justification should include calculations and which similarity theorem proves they are similar. If the triangles are not similar, show calculations and explain how you know. 19. State whether the triangles are similar. Show calculations. y -axis 15 (14, 15) G 10 (5, 8) D E (8,11) F (14, 11) 5 B (1, 6) C (5,6) x-axis

8 Geometry 2 nd Semester Review Packet Name PART 2: Chapter 5 1. If these were ¼-inch by ¼-inch squares, estimate the area of each blob. The second blob is a scaled copy of the first blob, scaled by a factor of Find the area of the following regular polygon:

9 3. A regular octagon has side lengths 24 inches. The length of its apothem is about inches. Find its area. 4. The area of a regular nonagon is about square centimeters. The length of its apothem is about centimeters. Find the length of each side of the nonagon. Show your calculations and include units. 5. A pizza has a diameter of 12 inches. Scale Ella knows that 4 th Period geometry is a hungry bunch, so she scales the pizza by a factor of 4. What is the area of the new pizza? For full credit, find it using the circumference and radius of the pizza.

10 6. Find the area of a circle whose radius is 6 and whose circumference is Find the scale factor and areas of these two circles: Diameter = 22 Radius = 6 8. Find the area of the sector. Show your calculations and include units cm 9. Find the area of the following sector:

11 10. Find the circumference of a circle whose radius is 7cm: 11. Find the area of a circle whose radius is 10 miles 12. Find the area of a circle whose diameter is 10 miles 13. Find the area of a circle whose circumference is 10π miles 14. Find the circumference of a circle whose radius is 5: 15. Given a circle with the following dimensions, find the exact circumference. a. radius 15 in b. diameter 2 cm

12 16. Find the circumference of a circle whose radius is 17 inches: 17. The area of a circle is 144π meters. Find the arc length of a 60 sector. 18. Find the length of each arc shown. a. b. 19. a. Find the measure of arc BC A C b. Find the length of arc BC 7cm D B

13 20. a. Find the measure of arc AB. A cm B b. Find the length of AB. 21. Find the measure of the central angle in degrees. Show your calculations. 20π 30 cm 22. The length of arc AC is 28 cm. Find the measure of the central angle AQC in radians and degrees: A 28cm Q 7cm C D B

14 23. Find the measure (in radians) of an angle that is 56 degrees: 24. What is the measure of the arc? What is the length of the arc? Measure = Length = 25. In general, what is the relationship between the central angle and the measure of the arc it intercepts? 26. Find the measure of x: 0 x 0 50

15 27. Find m ABC. a.) b.) 28. In the figure, find the values of x and y. A 29. a. Name 2 major arcs: C b. Name 2 minor arcs 7cm D B

16 30. How far is a 12 cm chord from the center of the circle whose radius is 10 cm? Show pictures and justify your response for full credit. 31. How long is a chord if it is 24 centimeters from the center of a circle whose radius is 26cm? Show pictures and justify your response for full credit. 32. What is the radius of a circle that has a 16cm chord that is 30cm from the center of the circle? Show pictures and justify your response for full credit. 33. What is the radius of a circle that has a 10cm chord that is 6cm from the center of the circle? Show pictures and justify your response for full credit.

17 34. What is the measure of: a. AOC A b. ABC O C c. Arc CD B d. CBD D 35. This circle is centered at O. Showing work for credit, find the measure of: a. GDH b. DKM D G K B 14 E 0 H 0 46 M O c. Arc BJL A L J 0 80

18 36. This circle is centered at O. Showing work for credit, find the measure of: a. GDH b. DKM D G K B 14 E 0 H 0 26 L M O 0 80 c. Arc BJL A J 37. Find LM and JK, with the givens marked on the diagram. All lengths are marked on the diagram. B G H 5 M 15 9 L 12 J K N

19 38. Find LM and NK, with the givens marked on the diagram. All lengths are marked on the diagram. B G H 5 M L 12 J 10 K N 39. Find the probability of dropping a coin on the circle and having it land in the square: 40. Find the probability of dropping a coin on the square and having it land in the circle:

20 Geometry 2 nd Semester Review Packet PART 3: Chapter 6 Find all the missing variables. Name b x Find the values of x, y, and z. 6 18

21 5. Find the values of x, y, and z Find the values of the variables in each triangle. Give exact values. a. b. a b c c. d. 18 e 30 f d 7. Find the values of x and y. a. b.

22 8. Find the exact value of each of the identified angles/sides: A 120 AC= CB= m A= C 30 B E b.) 24 D 45 F DE= DF= m F = c.) G 16 GJ= JH= m G= m H = J H d.) K KM= LM= m M = L M

23 _ 9. Find the value of each variable. Give exact answers. a. B b _ c d a c. d. a 60 b c Find the value of each variable. The triangles are not drawn to scale. a. b. 7 z 10 y c. d. 7 y 7 53 x 34

24 11. A lighthouse watch person observes that there is a 12 angle of depression between the horizontal and line of sight to a ship. If the keeper is 19 m above the water, how far is the ship from shore? 12 Ship 12. Find the area of the triangle below Two sides of a triangle have lengths 3 cm and 7 cm. The angle between them measures 130. Find the length of the third side.

25 14. D = 27 E DE = 6 D DF = 10 F Find the area of this triangle to the nearest tenth.

26 Geometry 2 nd Semester Review Packet PART 4: Chapter 7 Name 1. Graph the quadrilateral ABCD with A 2,2, B 5,1, C 6,4, and 3,7 D. a. ABCD is translated to produce A B C D. The translation is defined by the following rule. x, y x 7, y 2. Graph A B C D. b. Describe the translation in words. 2. a. Graph the function y 2 x. y x 3. b. Graph the function 2 c. Describe the graph of 2 of the graph of y 2 x. y x 3 as a transformation

27 Graph Rectangle ABCD with A: (-3, 6), B: (2, 6), C: (2, 2), and D: (-3, 2). 3. Reflect the rectangle over the x-axis. Name the new image IJKL. 4. Reflect the original rectangle ABCD over the line x 3. Name the new image A B C D. Reflect that image over the line y 1. Name the final image A B C D.

28 5. a. Reflect AB with endpoints A 2,5 and 0,4 the image. B over the line with equation y = 5. Write coordinates of the endpoints of y b. Now reflect the image of AB over the line with equation y = 2. Write the coordinates of the endpoints of this new image. x c. Describe a single transformation that maps AB onto the final image.

29 6. For the points A(-5,6) and B(15,-54) a. Find the distance between A and B b. Find the midpoint of AB c. Write the equation of a line that passes through A and B d. Write an equation of a line that is parallel to AB e. Write an equation of a line that is perpendicular to AB 7. If C(-2, 14), are A, B, and C collinear? Support your solution with a numerical justification