Transformations, Congruence and Similarity

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.

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)

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?

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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

Consider the triangles shown. Which can be used to prove the triangles are congruent?

• SSS

• ASA

• SAS

• AAS

In this diagram, DE is congruent to JI and angle D is congruent to angle J. Which additional information is sufficient to prove that ∆DEF is congruent to ∆JIH?

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In this figure, LN is perpendicular to KM. What additional information would a student need to prove ∆KLN~∆MLN?

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In this diagram, STU is an isosceles triangle where ST is congruent to UT. The paragraph proof shows that angle S is congruent to U. Which step is missing in the proof?

• CPCTC

• Reflexive Property

• Definition of right angles

• Angle Congruence Postulate

The following is a proof of the Pythagorean Theorem. Which reason justifies step 2?

• Triangle proportionality theorem.

• Corresponding sides of similar triangles are proportional.

• Corresponding sides of similar triangles are congruent.

• Triangle mid-segment theorem.