Triangle Similarity Postulates

The video tutorial covers methods to prove triangle similarity, including angle-angle, side-angle-side, and side-side-side postulates. It provides examples and practice problems to help understand these concepts. The tutorial also explores using parallel lines and proportions to determine triangle similarity and solve for missing parts.

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

• Angle-Side-Angle (ASA)

• Angle-Angle (AA)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

In the Angle-Angle (AA) similarity postulate, what must be true for two triangles to be similar?

• One angle and two sides of one triangle are congruent to one angle and two sides of another triangle.

• All three sides of one triangle are proportional to all three sides of another triangle.

• Two angles of one triangle are congruent to two angles of another triangle.

• Two sides of one triangle are proportional to two sides of another triangle.

If two triangles have two pairs of corresponding angles that are congruent, which similarity postulate can be used?

• Angle-Side-Angle (ASA)

• Angle-Angle (AA)

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

If two triangles are similar by the Angle-Angle (AA) postulate, what can be said about their corresponding sides?

• They are parallel.

• They are proportional.

• They are congruent.

• They are equal in length.

What is the key requirement for the Side-Angle-Side (SAS) similarity postulate?

• Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

• Two angles of one triangle are congruent to two angles of another triangle.

• Two sides and the included angle of one triangle are proportional to two sides and the included angle of another triangle.

• All three sides of one triangle are proportional to all three sides of another triangle.

Which of the following is a correct statement about the Side-Angle-Side (SAS) similarity postulate?

• It requires two pairs of corresponding angles to be congruent.

• It requires all three sides of one triangle to be proportional to all three sides of another triangle.

• It requires two angles and the included side of one triangle to be congruent to two angles and the included side of another triangle.

• It requires two sides and the included angle of one triangle to be proportional to two sides and the included angle of another triangle.

For the Side-Side-Side (SSS) similarity postulate, what must be true?

• Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

• All three sides of one triangle are proportional to all three sides of another triangle.

• Two sides and the included angle of one triangle are proportional to two sides and the included angle of another triangle.

• Two angles of one triangle are congruent to two angles of another triangle.

In a pair of similar triangles, if one triangle has sides of lengths 10, 15, and 20, and the other has sides of lengths 5, 7.5, and 10, which similarity postulate is used?

• Angle-Angle (AA)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

Which similarity postulate would you use if you know all three sides of two triangles are proportional?

• Angle-Angle (AA)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

In a problem involving similar triangles, if the ratio of two corresponding sides is 3:4, what is the ratio of their perimeters?

• 1:1

• 3:4

• 9:16

• 4:3