Proving Triangle Similarity: SSS and SAS Methods

The video tutorial covers the concepts of triangle similarity using the SSS and SAS theorems. It explains how to determine if triangles are similar by comparing proportional side lengths and angles. The tutorial includes examples to illustrate the application of these theorems, helping students understand how to identify similar triangles. The session concludes with a practice problem for students to solve independently.

What does the SSS similarity theorem state?

• If two triangles have three pairs of congruent sides, they are similar.

• If two triangles have three pairs of proportional sides, they are similar.

• If two triangles have two pairs of congruent angles, they are similar.

• If two triangles have one pair of congruent sides, they are similar.

In the SSS similarity theorem, what must be true about the side lengths of two triangles?

• The side lengths must be equal.

• The side lengths must be different.

• The side lengths must be proportional.

• The side lengths must be congruent.

Which of the following pairs of triangles are similar based on the given side lengths: Triangle PQR (15, 25, 30) and Triangle XYZ (21, 35, 42)?

• They are similar by the AA similarity theorem.

• They are similar by the SAS similarity theorem.

• They are similar by the SSS similarity theorem.

• They are not similar.

What is the simplified ratio of the sides 25 and 35?

• 5/6

• 5/9

• 5/8

• 5/7

What does the SAS similarity theorem state?

• If two triangles have two pairs of congruent sides, they are similar.

• If two triangles have two pairs of proportional sides and the included angle is congruent, they are similar.

• If two triangles have two pairs of congruent angles, they are similar.

• If two triangles have one pair of congruent sides, they are similar.

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

• The included angle must be different.

• The included angle must be equal.

• The included angle must be proportional.

• The included angle must be congruent.

Given that angle X is congruent to angle M and the sides around these angles are proportional, what can be concluded about triangles XYZ and MNP?

• They are congruent.

• They are similar by the SAS similarity theorem.

• They are similar by the SSS similarity theorem.

• They are not similar.

If SR is 24 and PN is 18, what is the simplified ratio?

• 3/4

• 4/3

• 3/2

• 2/3

Which similarity theorem would you use if you know two angles of one triangle are congruent to two angles of another triangle?

• AA

• SAS

• None of the above

• SSS

What is the ratio of RT to NQ if RT is 28 and NQ is 21?

• 2/3

• 4/3

• 3/4

• 4/5