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2 5 th Six Weeks Geometry PAP MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Feb Quiz Workday Arc Length and Sectors CW: Finish Arc length & Sector Area HW: Video Area Regular Polygons 13.3 Area of Regular Polygons day 1 Warm up 2 CW: Regular Polygons Day 1 HW: Video Regular Polygons day Area of Regular polygons 2 and 3 Warm up 3 CW: Regular Polygons 2 & 3 HW: Complete classwork 13.3 Area of Regular polygons 2 and 3 Warm up 3 CW: Regular Polygons 2 & 3 HW: Complete classwork Exploring Solids CW: pages 3-4 HW: Study Test #13 HW: EOC #4 Watch Video 14-4 Part A 14-4 Part A Volume of Prisms CW: pages 5-6 odd, 7-8 all HW: Watch Video 14-5 Part A 14-4 Part A Volume of Prisms CW: pages 5-8 HW: Watch Video 14-5 Part A 29 March /14-5/14-6 Part B Volume of Cylinders, Cones, and Spheres CW: pages odd HW:No Video, work on classwork. Workday Warm up 2 CW: Complete worksheets HW: Watch Video Surface Area and Volume of Similar Solids Warm up 3 CW: pages HW: complete CW 14-7 Surface Area and Volume of Similar Solids Warm up 3 CW: pages HW: complete CW Part A Surface Area of Prisms CW: HW: Study Test #14 HW:EOC #5. Watch Video 14-3 Part B 14-3 Part A Surface Area of Pyramids CW: pages HW: No Video 14-3 Part B Surface Area of Pyramids CW: pages HW: No Video Review Formula Quiz CW: Review EOC #3 Due HW: Watch Video 14-1 Exploring Solids, Review 14-5 Part A Volume of Pyramids Warm up 1 CW: pages 9-10 HW: Watch Video 1-4/14-5/14-6 CW:Review EOC #4 Due Formula Quiz HW: Watch Video 14-2 Part B 14-2 & 14-3 Part A Workday Surface area of Prisms and Pyramids Celebrate Approximately Pi Day Spring Break Spring Break Spring Break Spring Break Spring Break Part B Surface area of Spheres CW: pages HW: Video 14-2/14-3 Part B Surface area of Cylinders and Cones CW: pages HW: Study for formula Quiz Quiz Formula Quiz EOC #5 due Mix of all figures Review Day Quiz Formula Quiz EOC #5 Due Mix of all figures Review Day School Holiday 28 Per: Per: 2,4 30 Per: Per: 4,6 April 1 Per:1,3,5,7 Test #15 Give out EOC #6 HW:Watch Video Reflections(2) Translations(1,5,7) 8-2 Reflections CW: pages 6-7 HW:Watch Video Translations (2) 8-1 Translate figures CW: Pages 4-5 HW:Watch Video Reflections (1,5,7) Rotations (2) 8-2 Reflections CW: pages 6-7 HW:Watch Video Rotations(1,5,7) 2

3 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY April Rotations CW:pages 8-10 HW: Try rotations about a point that is not the origin. Geometry PAP 6 th Six Weeks Rotations about a point not the origin 8-4 Symmetry CW: pages HW:Watch Video Dilations 8-7 Dilations CW:pages HW Complete classwork Need for class the next day: red & blue pen, highlighter, pencil 8-7 Dilations CW: pages HW: Complete classwork Need for class the next day: Red & blue Pen, highlighter, pencil Quiz 9.5 Compositions of Transformations CW:pages HW: Complete classwork, makes sure EOC #6 is complete Review EOC #6 Due Formula Quiz #6 Test #16 Give out EOC # Vocabulary with Circles 10.2 Find Arc Measures 10.1 Vocabulary with Circles 10.2 Find Arc Measures 10.3 Properties of Chords Quiz HW: HW: Pg 1-3 HW: Pg Use Inscribed angles and Polygons 10.5 Other Angle relationships in Circles 10.6 Find Segment lengths in Circles 10.7 Write and graph equations of Circles 10.6 Find Segment lengths in Circles 10.7 Write and graph equations of Circles Review EOC #7 Due Formula Quiz HW: End of Year Wrksht #1 Test #17 End of Year Wrksht #2 End of Year Wrksht #2 End of Year Wksht #3 Give out EOC #8 HW: HW: May End of Year Wksht #4 End of Year Wksht #5 End of Year Wksht #5 End of Year Wksht #5 End of Year Wksht # Review EOC #8 Due Formula Quiz Test #18 Give out EOC #9 Review for final Review for final Review for final ,3,5,7 19 late 2,4, Review for final EOC #9 Due Review for final Formula Quiz Seniors (3 rd & 5 th ) Review for final Seniors (4 th & 6 th ) Review for Final 7 th Final Exam st and 2 nd Final exam (all) 3 rd and 4 th Final Exam 5 th and 6 th Final Exam Teacher Workday Holiday 3

4 8-1 Translations and Vectors* Use the translation x, y x 5, y 8. 1) What is the image of B 4,2? 2) What is the image of 1,5 D? 3) What is the preimage of F 3, 4? 4) What is the preimage of 7, 5 H? 5) What is the image of J 0,2? 6) What is the preimage of 4,6 Write a rule for the translation. 7) 1 units to the left and 1 unit up 8) 3 units down 9) 7 units to the left and 4 units down 10) 10 units right and 8 units up K? A B C is the image of ABC after translation. Write a rule for the translation. Then verify that the translation is an isometry. (Find the length of each segment) 11) 12) Name the vector and write its component form. 13) 14) 15) 4

5 Draw the following vectors* 16) DV 2, 5 17) HY 0,3 18) PU 4, 3 ABC with vertices A 2,4, B 6,2, C 3, 2 is translated to A B C. Determine the translation using vector in component form, and determine the coordinates of the remaining vertices. 19) A 5,5 20) B 2, 5 21) C 4, 5 22) B 8,6 In Exercises 23-25, use the following information. Skiing A skier travels from point A to point D. At point B and C, the skier changes direction, as shown in the diagram. The distance in the diagram are in kilometers. 23. Write the component form of AB, BC, and CD. 24. What is the total distance the skier travels? 25. Suppose the skier went straight from A to D. Write the component form of the vector that describes this path. What is the distance? 5

6 8-2 Reflections Graph the reflection of the polygon in the given line. 1) 2) 3) 4) Find the coordinates of the image without using a coordinate plane. Then check you answer by plotting the image and preimage on a coordinate plane. 5) M 3,4 reflected in the line y 1. 6) 2,2 7) P 2,3 reflected in the line x 3. 8) 5, 2 Use the diagram to name the image of Segment 1 after the reflection. 9) Reflection in the x-axis 10) Reflection in the y-axis 11) Reflection in the line y x 12) Reflection in the line y x 13) Reflection in the y-axis, followed by a reflection in the x-axis 14) Reflection in the x-axis, followed by a reflection In the y-axis N reflected in the line y 1. Q reflected in the line x 3. 6

7 *Find the coordinates of each image. 15. R x-axis(a) 16. R y-axis(b) 17. R y = 1(C) 18. R x = 1(D) 19. R y = 1(E) 20. R x = 2(F) *Coordinate Geometry Given points M(3, 3), N(5, 2), and O(4, 4), graph ΔMNO and its reflection image as indicated. 21. R y-axis 22. R x-axis 23. R x = R y = 2 The vertices of ABC are A 4,4, B 0,7 the second line. Graph A B C and A B C., and 1,3 C. Reflect ABC in the first line. Then reflect A B C in 25) In y 4, then in x 1 26) In x 3, then in y 5 7

8 8-3 Rotations Math the diagram with the angle of rotation. A. 60 B. 130 C. 95 1) 2) 3) Rotate the figure the given number of degrees about the origin. List the coordinates of the vertices of the image. 4) 90 5) 180 6) 270 Point O is the center of regular hexagon BCDEFG. Find the image of the given point or segment for the given rotation. 7. r (120, O)(F) 8. r (180, O)(B) 9. r (300, O)( BG) 10. r (360, O)( CD) 11. r (60, O)(E) 12. r (240, O)( FE ) 8

9 For Exercises 13 15, ΔABC has vertices A(2, 2), B(3, 2), and C( 1, 3). 13. Graph r (90º, O)( ABC). 14. Graph r (180º, O)( ABC). 15. Graph r (270º, O)( ABC). 17. The vertices of PQRS have coordinates 18. The vertices of r (90º, O) (KLMN) have coordinates P( 1, 5), Q(3, 4), R(2, 4), and S( 3, 2). K ( 3, 2), L (2, 3), M (4, 2), and N ( 2, 4). What are the coordinates of the vertices What are the coordinates of the vertices of KLMN? of r (270º, O)(PQRS)? For Exercises 19 21, ABCD has vertices A(1, 1), B(1, 3), C(4, 3), and D(4, 1). 19. Graph r (90º, O)(ABCD). To start, graph ABCD. A = r (90º, O)(A) = ( 1, ) B = r (90º O)(B) = ( 3, ) C = r (90º, O)(C) = (, 4) D = r (90º, O)(D) = (, 4) Then graph A, B, C, and D. 9

10 For Exercises 19 21, ABCD has vertices A(1, 1), B(1, 3), C(4, 3), and D(4, 1). 20. Graph r (180º, O)(ABCD). 21. Graph r (270º, O)(ABCD). 22. The vertices of ΔPQR have coordinates P(1, 5), Q(3, 1), and R( 2, 1). What are the coordinates of the vertices of r (90º, O)(ΔPQR)? Find the value of each variable in the rotation. 23) 24) 25) 10

11 8-3 Worksheet Rotations of figure through a point that is not the origin* Directions: Rotate each figure about point C, by the indicated degree measures. Make sure to list the first transformations as prime and second transformation as double prime. 1. Figure B 2, 1, A 5, 3, 1, 4 counter clockwise around the point C 1,1. D rotated 90 and Figure S 1,4, Q 3,2, U 6,5, 4,7 counter clockwise around the point C 0,1. A rotated 180 and

12 3. Figure D 2,6, E 5,6, 5,2 counter clockwise around the point C 3,1. F rotated 90 and Figure T 3, 1, R 1, 1, A 1, 4, 5, 4 counter clockwise around the point C 2,1. P rotated 90 and

13 Worksheet 8-4 Symmetry Tell what type(s) of symmetry each figure has. If it has line symmetry, sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation Determine how many lines of symmetry each polygon has. Include a sketch to support your answer. 9. regular quadrilateral 10. regular pentagon 11. regular hexagon 12. regular octagon 13. Make a Conjecture What is the relationship between the number of sides of a regular polygon and the number of lines of symmetry? 14. How many lines of symmetry are found in a regular polygon with 40 sides? Tell whether each three-dimensional object has reflectional symmetry in a plane, rotational symmetry about a line, or both. 15. a light bulb 16. a pair of pants 17. a rectangular table 18. a round table 19. a sand dollar 20. butterfly 13

14 Worksheet 8-5 Composite Transformations The vertices of ABC are A 3, 1, B 7,1, and 5, 4 transformations in the order they are listed. 1) 2) C. Graph the image of ABC after a composition of the

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18 Worksheet * *

19 (I would suggest doing these on your own graph paper, so that you can use a 1 to 1 scale.) 19

20 * *

21 Review Chapter 9 Transformations Give the vertices of the image after it is reflected across the given line. 1) A 2,1, B 6,1, C 4,3 across the x-axis. 2) N 1,2, P 3,5, Q 3,7, R 1,6 across the line y x. 3) A 4,2, B 7, 1, C 0,1 across the y-axis. Draw the line of symmetry for each figure, tell whether it has rotation symmetry. 3) 4) 5) 6) Name the vector, and write vector in component form and give magnitude. D F B A C E Translate the following figures given the vertices and the motion rule. 7) D 2,4, E 4,1, F 4, 2 ; 8) J 3, 1, K 2, 3, L 1, 3, M 2, 1 x, y x 2, y 2 x, y x 1, y 4 Tell what kind of transformation each pair of figures simulates. 9) 10) 11) 12) 21

22 Rotate the following figure about the origin by the given angle measure. 13) P 4, 3, Q 2, 3, R 1, 2, S 3,0 14) A 4,4, B 2,1, C 0,3 180 counterclockwise rotation 90 clockwise rotation Draw the image of the figure with the given vertices under a dilation with the given scale factor centered at the origin. 15) D 0,2, E 0,0, F 2,1, G 2,2 16) A 4,4, B 2,0, C 0,0 Scale factor: 2 scale factor: ½ Solve the following matrices. 17) 18) 19) 20) 22

23 Do the following composite transformations: 21) Translate x, y x 4, y 1, 22) Rotate 180 counterclockwise, Reflect across the x-axis. Reflect across the y-axis C A B C B A 23) Reflect x 1, 24) Reflect y x, Rotate translate x, y x 2, y 4 90 counterclockwise. A A B D C B C 25) 26) Find the value of x and y? Make sure you can rotate a figure about a point that is not the origin and that you can dilate a figure through a point that is also not the origin. 23

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