Lesson 11

Similarity

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Problem 1

Each diagram has a pair of figures, one larger than the other. For each pair, show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one.

Coordinate plane, x 0 to 4, y 0 to 6. Line through point A, the origin, C at 1 comma 2, E at 3 comma 6. Segments connect A, & C to point B at 1 comma 0. Segments connect E & C to point F at 3 comma 2.
Two triangles on a circular grid. Ask for further assistance.

Solution

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Problem 2

Here are two similar polygons.

Measure the side lengths and angles of each polygon. What do you notice?

figure ABCD and figure EFGH on a grid.

Solution

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Problem 3

Each figure shows a pair of similar triangles, one contained in the other. For each pair, describe a point and a scale factor to use for a dilation moving the larger triangle to the smaller one. Use a measurement tool to find the scale factor.

Triangles A, B C, and A prime B C prime. A prime lies on side A, B. C prime lies on side B C.
Triangles A, B C, and A, B prime C prime. B prime lies on side A, B. C prime lies on side A, C.

Solution

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Problem 4

Describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.

two of the same figure on a square grid in different orientations and position

 

Solution

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(From Unit 1, Lesson 3.)

Problem 5

  1. Draw the translated image of \(ABCDE\) so that vertex \(C\) moves to \(C’\). Tracing paper may be useful.
    Pentagon A B C D E and point C prime. Segment B C is the base of the pentagon and point E is the top. Point C prime is to the right of the pentagon.
  2. Draw the reflected image of Pentagon \(ABCDE\) with line of reflection \(\ell\). Tracing paper may be useful.
    Pentagon \(A\) \(B\) \(C\) \(D\) \(E\) and line \(l\). Segment \(B\) \(C\) is the base of the pentagon and point \(E\) is the top. Line \(L\) is vertical and is to the right of the pentagon.
  3. Draw the rotation of Pentagon \(ABCDE\) around \(C\) clockwise by an angle of 150 degrees. Tracing paper and a protractor may be useful.
    Pentagon A B C D E. Segment B C is the base of the pentagon and point E is the top.

Solution

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(From Unit 1, Lesson 2.)