Congruency and Similarity Statements

Determine if the two figures are congruent by using transformations. If so, explain the transformation or transformations that map the first figure onto the second figure.

• congruent; a counterclockwise rotation of 90° followed by a translation

• congruent; reflection

• congruent; translation

• not congruent

Determine if the two figures are congruent by using transformations. Explain your reasoning

• congruent; a rotation

• not congruent

• congruent; a reflection followed by translation

• congruent; a reflection

Which of the following transformations produces a figure that is congruent to the original figure?

• Rotations

• Reflections

• Translations

• Dilations

The vertices of ∆JKL, have coordinates J(5, 1), K(−2, −3), and L(−4, 1). Under which transformation is ∆J ′K ′L ′ not congruent to ∆JKL?

• A. A translation of two units to the right and two units down.

• B. A counterclockwise rotation of 180 degrees around the origin.

• C. A reflection over the x-axis

• D. A dilation with a scale factor of 2 and centered at the origin.

Triangle ABC was rotated 90 degrees counterclockwise around the origin. Which line segment must be congruent to line segment AB?

• Line segment OH

• Line segment TO

• Line segment TH

• The triangles are congruent to each other.

• The area and perimeter of these triangles are the equal.

What transformation shows that these triangles are congruent?

• reflection

• rotation

• dilation

• translation

If you rotate this figure counterclockwise as shown, will it produce a congruent figure?

• yes

• no

The two triangles are

• not congruent.

• congruent by a translation transformation.

• congruent by a reflection transformation.

• congruent by a rotation transformation.

Diego made the shape on the left, and Elena made the shape on the right. Each shape uses 5 circles. Select all the true statements.

• Elena’s design is a translation of Diego's design.

• Diego’s design is congruent to Elena’s design.

• The smallest circle in Diego's design is congruent to the smallest circle in Elena’s design.