Similarity Review

A sequence of transformations occurred for ∆ABC to become ∆A’’B’’C’’. Which of the following statements are true about the sequence of transformations graphed below.

• ∆A’’B’’C’’ is similar to ∆ABC.

• ∆A’B’C’ is congruent to ∆ABC.

• ∆A’’B’’C’’ is a rotation of ∆A’B’C’.

• The scale factor of the dilation applied to produce ∆A’B’C’ is ½.

• The scale factor of the dilation applied to produce ∆A’B’C’ is 2.

Trapezoid PQRS is resized by a scale factor of 3/2 about the origin and then translated 5 units up into the trapezoid P’Q’R’S’. What are the coordinates of P’?

• (3, 2)

• (6, -3)

• (6, 2)

• (3, -2)

Which of these statements is true about the two graphed rectangles?

• They are similar because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

• They are similar because one can be obtained by dilating the other about the origin with a scale factor of 2.

• They are not similar because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

• They are not similar because one can be obtained by dilating the other about the origin with a scale factor of 2.

A student claims that if a triangle is rotated, reflected, or translated to produce another triangle, the

two triangles are similar. However, he says that if a triangle is dilated to produce another

triangle, the two triangles are not similar. Which of these statements are correct? Select three

that apply.

• The student is right in saying that if a trapezoid is rotated to produce another trapezoid, the two trapezoids are

  similar.

• The student is right in saying that if a trapezoid is reflected to produce another trapezoid, the two trapezoids are

  similar.

• The student is right in saying that if a trapezoid is translated to produce another trapezoid, the two trapezoids are

  similar.

• The student is right in saying that if a trapezoid is dilated to produce another trapezoid, the two trapezoids are not

  similar.

Dilate the triangle with a scale factor of 1/2. Which of these is not a coordinate of the image? Select all that apply.

• (0.5, 2.5)

• (-2, -2)

• (3, -2)

• (-5, -8)

• (2, 10)

Which sequence of transformations could be used to verify that triangle ABC is similar to DEF?

• Dilation by a scale factor of 2, followed by a rotation of 90^o clockwise, then a translation (x + 1, y + 1)

• Dilation by a scale factor of 2, followed by a rotation of 90^o clockwise.

• Dilation by a scale factor of 1/2, followed by a rotation of 90^o clockwise.

• Dilation by a scale factor of 1/2, followed by a rotation of 90^o counterclockwise.

A sequence of transformations is applied to a trapezoid. Which of the following statements represent a sequence of transformations where the resulting trapezoid is similar to the original trapezoid but has a smaller area than the original trapezoid? Select all that apply.

• A dilation about the origin by a scale factor of 1/2 followed by a reflection over the x-axis and a dilation about the origin by a scale factor of 1/4.

• A dilation about the origin by a scale factor of 1/3 followed by a rotation of 90˚ clockwise about the origin and a translation 4 units right.

• A reflection over the x-axis followed by a translation 4 units up and a dilation about the origin by a scale factor of 3.

• A rotation of 180˚ clockwise about the origin followed by a dilation about the origin by a scale factor of 5/2.

Suppose you are using transformations to show that two triangles are similar. Which of these pairs

of triangles would require that you use a dilation about the origin with a scale factor of 1/2 or 2?

Select two that apply.

• A(4, 2), B(1, 2), C(3, 6) - A'(8, 4), B'(2, 4), C'(6, 12)

• A(4, 2), B(1, 2), C(3, 6) - A'(6, 3), B'(2, 4)), C'(3, 9)

• A(4, 2), B(1, 2), C(3, 6) - A'(2, 1), B'(0.5, 1), C'(1.5, 3)

• A(4, 2), B(1, 2), C(3, 6) - A'(1, 2), B'(1, 3), C'(1.5, 14)

Suppose a triangle with vertices (-2, 5), (-1, -3), and (4, -1) were dilated, with the center of dilation at the origin and with a scale factor of 3. Which of these would be a vertex of the dilated figure? Select three that apply.

• (3, -9)

• (-6, 15)

• (12, -3)

• (3, 9)

• (-3, -9)

Mrs. Besson noticed that triangles ABC and DEF below are the same shape. What can she conclude based on her observation? Select 3 that apply.

• The measure of angle CAB is equal to the measure of angle FDE.

• The measure of angle ABC is equal to the measure of angle DFE.

• The measure of angle ACB is equal to the measure of angle FDE.

• The measure of angle ABC is equal to the measure of angle DEF.

• The measure of angle ACB is equal to the measure of angle DFE.