Transformations, Similarity, and Congruence

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

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

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

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

• SSS

• ASA

• SAS

• AAS

In this diagram, CD is the perpendicular bisector of AB. The two-column proof shows that AC is congruent to BC. Which theorem would justify step 6?

• AAS

• ASA

• SAS

• SSS

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

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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.

• Alternate interior angles are congurent

• Corresponding angles are congruent

• Vertical angles are congruent

• Alternate exterior angles are congruent

Choose all possible sequences of transformations that would map figure MATH to figure M'A'T'H'.

• Rotate 180 degrees

• Rotate 90 degrees clockwise, then reflect across the x-axis

• Rotate 90 degrees counter clockwise, then reflect across the y-axis

• Reflect over the line y=x

• None of the above