Exploring Similarity and Proofs in Geometry

What are the properties of similar triangles?

• Sides are equal and angles are different

• Sides are in proportion and angles are different

• Sides are in proportion and angles are congruent

• Sides are equal and angles are proportional

Which of the following is NOT a method to prove similarity in triangles?

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

• Angle-Angle (AA)

• Angle-Side-Angle (ASA)

In the SAS similarity theorem, what must be true about the sides and angle?

• The sides must be equal and the angle must be different

• The sides must be in proportion and the angle must be different

• The sides must be in proportion and the angle must be congruent

• The sides must be equal and the angle must be congruent

If AB/DE = AC/DF and angle A is congruent to angle D, which similarity theorem is being used?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Angle-Angle (AA)

In the SSS similarity theorem, what must be true about the sides of the triangles?

• All sides must be in proportion

• Two sides must be in proportion

• One side must be in proportion

• All sides must be equal

If AB/DE = 9/3, AC/DF = 6/2, and BC/FE = 12/4, what is the ratio of the sides?

• 4

• 3

• 2

• 5

In the AA similarity theorem, how many pairs of angles need to be congruent?

• Three pairs

• Two pairs

• Four pairs

• One pair

Which similarity theorem is used when no side lengths are given?

• Angle-Side-Angle (ASA)

• Angle-Angle (AA)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

What is the first step in a two-column similarity proof?

• Prove vertical angles are congruent

• State the given information

• Prove alternate interior angles are congruent

• Prove the sides are in proportion

Why are angles 3 and 4 congruent in the similarity proof?

• They are alternate interior angles

• They are supplementary angles

• They are corresponding angles

• They are vertical angles