Triangle Similarity

Match the following

• Triangle Proportionality Theorem

• If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

• Angle Bisector Theorem

• two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional

• SAS Similarity Theorem

• an angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle

• AA Similarity Postulate

• in any triangle, if a line intersects two sides of the triangle and is parallel to the third, then the intersecting line divides the sides proportionally

• SSS Similarity Theorem

• two triangles are considered similar if at least two corresponding angles are congruent

Match the following

• Corresponding Angles Theorem

• 
• Same Side Interior Angles Theorem

• 
• Alternate Interior Angles Theorem

• 
• Alternate Exterior Angles Theorem

• 

Nick performs a transformation on a triangle. The resulting triangle is similar but not congruent to the original triangle. Which transformation did Nick perform on the triangle?

• Dilation

• Reflection

• Rotation

• Translation

A figure is shown where AB||CD. Complete the statement to describe the relationship between the two triangles.
△APB is (a)   to the △DPC because △APD is a ​ (b)   of △DPC.

• similar
• not similar
• rotation & a dilation
• rotation & a reflection
• translation & a dilation
• reflection & a translation

Which transformation on ∆XYZ results in a triangle that is similar, but not congruent to ∆XYZ?

• a translation 3 units to the right

• a reflection across the line y=-2x+3

• a rotation 90 degrees around the origin

• a dilation centered at the origin with a scale factor to 2

Two similar triangles, ∆ABC & ∆JKL are shown. What is the length of side JL?

Mathematical Equivalence

ON

Triangle XYZ is shown. Which triangle must be similar to the triangle XYZ?

• a triangle with two angles that measure 40°

• a triangles with angles that measure 40° & 60°

• a scalene triangle with only one angle that measures 100°

• an isosceles triangle with only one angle that measures 40°

Mathematical Equivalence

ON

Megan dilates ∆JLK about point J by a scale factor of ⅗ to create ∆JNO. What is the measure, in degrees, of ∠O.

Mathematical Equivalence

ON