SAS Similarity Theorem

What does SAS stand for in the SAS Similarity Theorem?

• Sum-Addition-Subtraction

• Square-Area-Square

• Sine-Adjacent-Sine

• Side-Angle-Side

State the SAS Similarity Theorem.

• If two triangles have two pairs of sides in the same ratio and the included angles are congruent, then the triangles are similar.

• If two triangles have two pairs of sides in the same ratio and the included angles are not congruent, then the triangles are similar.

• If two triangles have two pairs of sides in different ratios and the included angles are congruent, then the triangles are similar.

• If two triangles have three pairs of sides in the same ratio and the included angles are congruent, then the triangles are similar.

If two triangles are similar, what can you say about their corresponding angles?

• Corresponding angles of similar triangles are always right angles

• Corresponding angles of similar triangles are always acute

• Corresponding angles of similar triangles are equal.

• Corresponding angles of similar triangles are always obtuse

If two triangles are similar, what can you say about their corresponding sides?

• The corresponding sides of similar triangles are proportional.

• The corresponding sides of similar triangles are equal in length.

• The corresponding sides of similar triangles are perpendicular to each other.

• The corresponding sides of similar triangles are parallel to each other.

In the SAS Similarity Theorem, if two angles of one triangle are congruent to two angles of another triangle, what can you conclude about the triangles?

• The triangles are equilateral.

• The triangles are right-angled.

• The triangles are similar.

• The triangles are congruent.

In the SAS Similarity Theorem, if the ratio of the lengths of the corresponding sides of two triangles is equal, what can you conclude about the triangles?

• The triangles are similar.

• The triangles are isosceles.

• The triangles are equilateral.

• The triangles are congruent.

If two triangles satisfy the SAS Similarity Theorem, what can you say about their corresponding angles and sides?

• Corresponding angles are not equal and corresponding sides are in proportion.

• Corresponding angles are equal and corresponding sides are in proportion.

• Corresponding angles are equal and corresponding sides are not in proportion.

• Corresponding angles are not equal and corresponding sides are not in proportion.

Explain how you can use the SAS Similarity Theorem to determine if two triangles are similar.

• Check if the triangles have the same perimeter

• Count the number of sides in each triangle and compare them

• Measure the angles of the triangles and compare them

• To determine if two triangles are similar using the SAS Similarity Theorem, you would need to compare the ratios of the corresponding sides and check if the included angles are congruent.

What are the conditions for two triangles to be similar according to the SAS Similarity Theorem?

• The corresponding sides are not in proportion

• The triangles have different perimeters

• Two pairs of corresponding angles are not congruent

• Two triangles are similar if two pairs of corresponding angles are congruent and the corresponding sides are in proportion.

Provide an example problem where you can apply the SAS Similarity Theorem to determine if two triangles are similar.

• An example problem could be: Triangle ABC has side lengths AB = 6, BC = 9, and angle B = 60 degrees. Triangle DEF has side lengths DE = 4, EF = 6, and angle E = 60 degrees. Determine if triangle ABC is similar to triangle DEF using the SAS Similarity Theorem.

• Triangle ABC has side lengths AB = 6, BC = 9, and angle B = 60 degrees. Triangle DEF has side lengths DE = 4, EF = 6, and angle E = 60 degrees. Determine if triangle ABC is similar to triangle DEF using the Pythagorean Theorem.

• Triangle ABC has side lengths AB = 6, BC = 9, and angle B = 60 degrees. Triangle DEF has side lengths DE = 4, EF = 6, and angle E = 30 degrees. Determine if triangle ABC is similar to triangle DEF using the SAS Similarity Theorem.

• Triangle ABC has side lengths AB = 6, BC = 9, and angle B = 90 degrees. Triangle DEF has side lengths DE = 4, EF = 6, and angle E = 60 degrees. Determine if triangle ABC is similar to triangle DEF using the SAS Similarity Theorem.