Lesson 11: Practice Problems

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.

  1. a. Triangle A (0,0) B (1,0) C (1,2) and larger triangle C (1,2) E (3, 6) F (3,2) with a line running through (0,0) through their hypotenuse's.
  2. b. A concentric grid with center A and triangle BCD and larger triangle B"C"D"

Problem 2

Here are two similar polygons.

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

Two figures, ABCD and a larger version EFGH

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.

  1. a. Triangle ABC and contained triangle A'BC'
  2. b. Triangle ABC and contained triangle AB'C'

Problem 4

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

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

Problem 5 From Unit 1 Lesson 2

  1. Draw the translated image of so that vertex moves to . Tracing paper may be useful.

    A pentagon, ABCDE. There is a point C" to the right of ABCDE.

  2. Draw the reflected image of Pentagon with line of reflection . Tracing paper may be useful.

    A pentagon, ABCDE, with line of reflection l vertically on the right side of ABCDE.

  3. Draw the rotation of Pentagon around clockwise by an angle of 150 degrees. Tracing paper and a protractor may be useful.

    A pentagon, ABCDE.