Proving Triangle Similarity: SSS and SAS Methods

The video tutorial covers triangle similarity using the SSS and SAS theorems. It explains how proportional corresponding side lengths and congruent angles can determine triangle similarity. The tutorial includes examples comparing triangles ABC, DEF, and GHJ, and solving for x to make triangles similar. It also discusses the SAS similarity theorem and applies it to construct a lean-to shelter.

What theorem can be used to prove that two triangles are similar if their corresponding side lengths are proportional?

• Angle-Side-Angle (ASA) Theorem

• Side-Angle-Side (SAS) Congruence Theorem

• Side-Side-Side (SSS) Similarity Theorem

• Angle-Angle (AA) Theorem

In the example, which triangle was found to be similar to triangle ABC using the SSS similarity theorem?

• Triangle XYZ

• Triangle KLM

• Triangle DEF

• Triangle GHJ

Why was triangle ABC not similar to triangle GHJ?

• Because their corresponding side lengths were equal

• Because their corresponding side lengths were not proportional

• Because their corresponding angles were not congruent

• Because their corresponding angles were not proportional

What is the value of x that makes triangles ABC and DEF similar?

• 8

• 7

• 6

• 5

Which method is used to prove that triangles are similar if an angle of one triangle is congruent to an angle of another triangle and the lengths of the sides including these angles are proportional?

• Angle-Side-Angle (ASA) Theorem

• Side-Side-Side (SSS) Similarity Theorem

• Angle-Angle (AA) Theorem

• Side-Angle-Side (SAS) Similarity Theorem

In the example, what was the scale factor from triangle GHJ to triangle KLM?

• 5/6

• 4/5

• 2/3

• 3/4

What is the first step in determining if the right end of the lean-to shelter is similar to the left?

• Measure the height of the tree branch

• Compare the lengths of the sides

• Calculate the area of the triangles

• Check if the angles are congruent

What is the ratio of the side lengths 6 to 9 in the lean-to shelter example?

• 4/5

• 2/3

• 1/2

• 3/4

In the lean-to shelter example, what is the ratio of the side lengths 10 to 15?

• 2/3

• 3/4

• 2/5

• 4/5

Can the right end of the lean-to shelter be constructed to be similar to the left end using SAS similarity?

• Only if the side lengths are equal

• Only if the angles are adjusted

• No

• Yes