Transformations, Similarity, and Congruence

Which transformation results in a figure that is similar to the original figure but has a greater area?

• A dilation of triangle QRS by a scale factor of 0.25

• A dilation of triangle QRS by a scale factor of 0.5

• A dilation of triangle QRS by a scale factor of 1

• A dilation of triangle QRS by a scale factor of 2

In the coordinate plane, segment PQ is the result of a dilation of segment XY by a scale factor of 1/2. Which point is the center of dilation?

• (-4, 0)

• (0, -4)

• (0, 4)

• (4, 0)

The smaller triangle is transformed to create the larger triangle. Which of these is the scale factor of the dilation center at the origin?

• 4

• 2

• 1

• 1/2

Look at quadrilateral QRST. What is the image of point R after a counterclockwise rotation of 270 degrees about the origin?

• (6, -3)

• (-3, 6)

• (-6, 3)

• (3, -6)

Which figure represents the dilation of GH about the origin by a scale factor of 2?

• 
• 
• 
• 

Which transformation of HIJ does NOT result in a congruent triangle?

• a reflection across the x axis, followed by a rotation of 180° about the origin

• a rotation by 180° about the origin, followed by a translation of 2 units left & 3 down

• a translation of 1 unit right and 2 units up, followed by a dilation by a factor of 3

• a dilation by a factor of 2, followed by a dilation by a factor of ½

In the triangles shown, ∆ABC is dilated by a factor of 2/3 to form ∆XYZ. Given that m<A=50° and m<B=100°, what is m<Z?

• 15 degrees

• 25 degrees

• 30 degrees

• 50 degrees

• 2.0

• 4.5

• 7.5

• 8.0

This is a proof of the statement “If a line is parallel to one side of a triangle and intersects the other two sides at distinct points, then it separates these sides into segments of proportional lengths." Which reason justifies Step 2?

• Alternate interior angles are congruent

• Alternate exterior angles are congruent

• Corresponding angles are congruent

• Vertical angles are congruent

Parallelogram FGHJ was translated 3 units down to form parallelogram F’G’H’J’. Parallelogram F’G’H’J’ was then rotated 90° counterclockwise about point G’ to obtain F’’G’’H’’J’’. Which statement is true about parallelogram FGHJ and parallelogram F”G”H”J”?

• The figures are both similar and congruent.

• The figures are neither similar nor congruent.

• The figures are similar but not congruent.

• The figures are congruent but not similar.