SAS Theorem

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.

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.

The SAS Theorem stands for

• The Side Angle Side theorem

• The Side Angle Six Theorem

• The Side Side Side theorem

Triangles must have _______________ to be congruent by the SAS theorem

• Two pairs of matching sides

• Three pairs of matching sides

• Two pairs of matching sides AND a matching pair of angles in between

• Two sides and an angle

Answer explanation

You don't just need 3 sides and angles total.... you need three PAIRS

(A pair = 2)

A pair of congruent sides

A pair of congruent angles in the middle

Another pair of congruent sides

What does x have to equal to make these congruent by the Side angle side theorem?

• 8 cm

• 10 cm

• 51 degrees

• 90 degrees

Which triangle congruence theorem proves the two triangles congruent?

• SSS

• SAS

• not enough information

Which statement is true?

• These triangles are congruent because of SSS

• These triangles are congruent because of SAS

• Not enough info

Answer explanation

You need three PAIRS of matching tally marks ....not 3 total. Three pairs is six tally marks total

Which statement is true?

• These triangles are congruent because of the SSS theorem

• These triangles are congruent because of the SAS theorem

• Not enough info

Answer explanation

To be congruent by SAS, the matching angles (arches) have to be in the middle of the tally marks (matching sides).

The arches in this question are not in the middle of the tally marks