Triangle Similarity Theorems: SSS, SAS, AA Explained

What does the Side-Side-Side (SSS) rule state about triangle similarity?

• Two triangles are similar if all three pairs of corresponding angles are equal.

• Two triangles are similar if one pair of corresponding sides is proportional.

• Two triangles are similar if two pairs of corresponding sides are proportional.

• Two triangles are similar if all three pairs of corresponding sides are proportional.

In the SSS rule, if triangle ABC has sides 8, 6, and 10, and triangle DEF has sides 4, 3, and 5, are the triangles similar?

• No, because the angles are not equal.

• Yes, because the sides are proportional.

• No, because the sides are not proportional.

• Yes, because the angles are equal.

Which of the following sets of side lengths would NOT make two triangles similar by the SSS rule?

• 24, 18, 30 and 12, 9, 15

• 16, 12, 20 and 8, 6, 10

• 12, 9, 15 and 3, 2.25, 5

• 8, 6, 10 and 4, 3, 5

What additional condition is required for the Side-Angle-Side (SAS) rule to determine triangle similarity?

• The triangles must be congruent.

• All three pairs of corresponding sides must be proportional.

• The included angle between the two sides must be equal.

• Two pairs of corresponding angles must be equal.

If two triangles have sides in the ratio 3:2 and the included angle is equal, are the triangles similar by the SAS rule?

• No, because the sides are not proportional.

• Yes, because the angles are equal.

• No, because the included angle is not equal.

• Yes, because the sides are proportional and the included angle is equal.

What does the Angle-Angle (AA) rule state about triangle similarity?

• Two triangles are similar if all three pairs of corresponding angles are equal.

• Two triangles are similar if all three pairs of corresponding sides are proportional.

• Two triangles are similar if one pair of corresponding sides is proportional.

• Two triangles are similar if two pairs of corresponding angles are equal.

If two triangles have angles 60° and 50° in common, are they similar by the AA rule?

• Yes, because two pairs of corresponding angles are equal.

• No, because the sides are not proportional.

• No, because the included angle is not equal.

• Yes, because all three pairs of corresponding angles are equal.

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

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Angle (AA)

• Side-Side-Angle (SSA)

In a practice problem, if two triangles have sides 50, 35, 40 and 40, 25, 30, are they similar by the SSS rule?

• Yes, because the included angle is equal.

• No, because the angles are not equal.

• Yes, because the sides are proportional.

• No, because the sides do not have the same ratio.

If two triangles have angles 60° and 50° in common, and the third angle is 70° in both, are they similar by the AA rule?

• Yes, because all three pairs of corresponding angles are equal.

• Yes, because two pairs of corresponding angles are equal.

• No, because the included angle is not equal.

• No, because the sides are not proportional.