ADV Math 8 Unit 1 Study Guide Transformations, Congruence, & Similarity
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1 Name Period ADV Math 8 Unit 1 Study Guide Transformations, Congruence, & Similarity MGSE8.G.1 Verify experimentally the properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines. 1. Identify the angle measure of the reflected right triangle given that A = 35. A B C List the measure of each angle. A = B = C = 2. If trapezoid ABCD is reflected over the y-axis and CB DA, is not? ' ' ' ' DA CB? Explain why or why C D D C B A A B 3. Which transformations are congruent to the original figure? Which are similar to the original figure? 4. In your own words, tell how reflections, translations, rotations, and dilations are transformed from the original figure? 5. How do you dilate a figure on the coordinate plane? 6. The following picture shows which transformation?
2 7. What type of transformation does the diagram represent? Which axis is the figure reflected across? MGSE8.G.2 Understand that a two dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8. What sequence of events transforms rectangle PQRS to P Q R S? 9. Why is rotating something 270º counterclockwise the same as rotating something 90º clockwise? MGSE8.G.3 Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. 10. If quadrilateral ABCD is translated 5 units left and 3 units down, what are the new coordinates?
3 11. If rectangle PQRS is rotated 180 clockwise around the origin, what are the new coordinates? Rotate it 180 counter-clockwise. 12. If rectangle PQRS is reflected across the y-axis, what are the new coordinates? Reflect across x- axis. 13. Jerry plots the point (1,2) on a coordinate grid for a scavenger hunt. He tells the participants how to get to the next coordinate by reflecting the point over the x axis and then translating it to the left 7 units. What coordinate should the participants go to next? Draw a diagram. 14. Quadrilateral ABCD is rotated 90 and then 270 counter-clockwise about the origin. Name the new coordinates. Original Coordinates A (3, 4) B (4, 6) C (8, 6) D (7, 4) 90 CC New Coord. A B C D 270 CC New Coord. A B C D 15. The point (-14, 13) in a triangle is reflected across the x-axis, then translated 5 units left and 6 units down. What is the new coordinate?
4 16. Point H at coordinate (7, -13) in a square is rotated 90 o counterclockwise then reflected over the x- axis. What is the new coordinate of Point H? 17. The restaurant, Couch s proposed a building location at the coordinates of (-5,2), (-1,2), (-5, 5), and (-1, 5). The company decides to move the location and the builder must re-position the building by rotating it 270 degrees clockwise. What would the new coordinates of the building be? Show all work algebraically then draw a diagram. 18. What is a dilation? 19. Fill in the blanks with reduced, enlarged or congruent: If the scale factor is 20%, the figure is. If the scale factor is 120%, the figure is. If the scale factor is 100%, the figure is. 20. A vertex of a rectangle on the coordinate plane is (-4, -2). The rectangle is dilated and the new coordinate of the vertex is (-1, 1 ). What was the scale factor of the dilation? 2 a. 4 b. 2 c. 1 d If triangle ABC is dilated by a scale factor of 200%, name the new coordinates. Dilate with a SF of
5 MGSE8.G.4 Understand that a two dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. 22. Determine the scale factor you would multiply the first figure by to get the second figure. 7 in. 11 in. a b. 11 c. 1 d A square has an area of 4 square cm. and a similar square has an area of 36 square cm. What is the scale factor for these similar squares? Draw the two squares and determine the length of the sides a. 36 b. 9 c. 4 d If FGH JKL, which of the following could not be true a. G K b. GH JK c. HG LK d. L H MGSE8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. 25. How many angles are formed when a transversal intersects 2 parallel lines? How many different angle measures will there be? 26. Name and draw a picture to show each special angle pair created when 2 parallel lines are cut by a transversal (there are 5 special angle pairs). 27. How can you prove 2 lines are parallel? 28. Using the figure to the right, name a pair of angles that are: a. Alternate interior b. Alternate exterior c. Same-side exterior d. Vertical e. Same-side interior f. Supplementary g. Corresponding 29. Given: PQ RS. What is m 1? P 65 Q R 1 S
6 30. Name two obtuse angles in the figure. V T W Q R S a. QRW, TRW b. SRW, VRW c. QRV, VRS d. QRT, TRS 31. In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. If m 2 = 30, find m a. 120 b. 150 c. 30 d In the figure, line m line n. Find the measure of 4. n p m a. 63 b. 117 c. 27 d Given: m n. What is the m 2? What is the relationship between the angles? 34. In the figure, line g line h. Find the measure of 2. f g h 6 a. 161 b. 29 c. 151 d. 19
7 35. Find m. A xº (3x - 70)º B C a. m = 40º b. m = 45º c. m = 35º d. m = 50º 36. Find the measure of Find n in the obtuse triangle. a. 24 b. 20 c. 160 d What is the sum of the interior angles of any triangle? 39. What is the sum of the exterior angles of any triangle? What is the relationship between an exterior angle of a triangle and the 2 opposite interior angles? 40. Find the missing angle measure In the diagram below, m a = 80 and ABC BCA. Determine m 1.
8 42. Find the measure of angle a. Explain how you found it. a Find the angle measures in the equilateral triangle. q q q a. q = 120 b. q = 180 c. q = 30 d. q = 60
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