GSE Math 7-8 Unit 4: Transformations Study Guide
Name ______
GSE8.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.
2.If trapezoid ABCD is reflected over the y-axis and ||, is ||? Explain why or why not?
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.Which one of the images can be rotated to match the letter J on the left?
6.Which one of the images can be reflected to match the letter Z on the left?
For numbers 7 – 9, name the transformation that maps:
7.ABCCDE
8.ABCDEF
9.PMRPMQ
GSE8.G.2Understand 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.
10.What sequence of transformationsmaps rectangle PQRS to PQRS?
GSE8.G.3Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using coordinates.
11.If quadrilateral ABCD is translated 5 units left and 3 units down, what are the new coordinates?
12.If rectangle PQRS is rotated 180° clockwise around the origin, what are the new coordinates? Rotate it 180° counter-clockwise.
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°, returned to the preimage, and then rotated 270 counter-clockwise about the origin. Name the new coordinates after the transformation from the preimage.
Original Coordinates / A (3, 4) / B (4, 6) / C (8, 6) / D (7, 4)90° C / A’ / B’ / C’ / D’
270° CC / A” / B” / C” / D”
15. Point H (7, -5) in a square is rotated 90o counterclockwise then reflected over the x-axis. What is Point H’?
16.A restaurant 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 coordinates for the new building then draw a diagram on the graph below.
GSE8.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.
17.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 .
18. 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,). What was the scale factor of the dilation?
- 4 b. 2 c. d.
19.If triangle ABC is dilated by a scale factor of 200%, name the new coordinates.
Dilate with a SF of .
20.Determine the scale factor you would multiply the first square by to get the second square.
21.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? (Hint: Draw the two squares and determine the length of the sides.)
a. 36 / b. 9 / c. 4 / d. 322. If , which of the following could not be true
a. / b. / c. / d.GSE8.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.
23.How many angles are formed when a transversal intersects 2 parallel lines? How many different angle measures will there be?
24.Name each special angle pair created when 2 parallel lines are cut by a transversal (there are 5 special angle pairs).
25.Using the figure to the right, name a pair of angles that are:
- Alternate interior
- Alternate exterior
- Same-side exterior
- Vertical
- Same-side interior
- Supplementary
- Corresponding
26.Given: . What is m∡1? ______
27.Name two obtuse angles in the figure.
28.In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. If m2 = 30, find m4.
29. In the figure, linem ||line n. What is the measureof 4?
30.Given: m || n. What is the m? What is the relationship between the angles? ______
31.In the figure, line g line h. Find the measure of 2.
32.Find the measure of ∡1. ______
33.Write and solve an equation to find the measure of angle n in the obtuse triangle below.
34.What is the sum of the interior angles of any triangle? ______
35.What is the sum of the exterior angles of any triangle? ______
36.What is the relationship between an exterior angle of a triangle and the 2 opposite interior angles? ______
37.Write and solve an equation to find the measure of the missing angle below in the obtuse triangle. ______
38.In the diagram below, m∡b = 60° andm∡c = 60°. Determine . ______
39.Find the measure of angle a. Explain how you found it. ______
40.What is the value of k? ______