1. What does AA similarity claim about triangles?
A. According to the AA similarity criterion, triangles with two pairs of congruent angles are similar
B. According to the AA similarity criterion, triangles with two pairs of congruent sides are similar.
C. According to the AA similarity criterion, triangles with two pairs of congruent angles are congruent.
D. According to the AA similarity criterion, triangles with two pairs of congruent sides are congruent.
2. Compare and contrast the AA similarity criterion with the ASA congruence criterion. Choose the correct answer.
A. Both criteria require that two pairs of sides be congruent, but for congruence you also need to know that the included angles are congruent, so that the figures are the same size. The AA similarity criterion shows only that the triangles are the same shape.
B. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same size.
C. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the non-included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape.
D. Both criteria require that two pairs of angles be congruent, but for congruence you also need to know that the included sides are congruent, so that the figures are the same size. The AA similarity criterion shows only that the two triangles are the same shape.
3. Given the image below, fill in the blanks to make a true sentence.
The triangles are------------- The similarity statement is--------------
Similar
not similar
△ABC ~ △FED
△ABC ~ △DEF
△ABC ~ △EFD
not needed as the triangles are not similar
4. If △ABC has interior angles such that m∠A=30° and m∠B=53° , then which of the following triangles must be similar to △ABC ? △MNP with m∠N=52° and m∠P=90△RSQ
with m∠R=43° and m∠S=79°
A. neither
B. Both
C. RSQ only
D. M N P only
5. In △JKL, m∠J=40° and m∠K=55°
In △MNP, m∠M=40° and m∠P=85°
A student concludes that the triangles are not similar. Do you agree or disagree? Why?
A. Disagree, by the Triangle Angle Sum Theorem, m∠N=45° , so the triangles are similar by the AA similarity criterion.
B. Agree, since m∠K≠m∠P , the triangles are not similar by the AA similarity criterion.
C. Agree, by the Triangle Angle Sum Theorem, m∠N=45° , so the triangle are not similar by the AA similarity criterion.
D. Disagree, by the Triangle Angle Sum Theorem m∠N=55° , so the triangles are similar by the AA similarity criterion.
1. A. According to the AA similarity criterion, triangles with two pairs of congruent angles are similar.
2. A. Both criteria require that two pairs of sides be congruent, but for congruence you also need to know that the included angles are congruent, so that the figures are the same size. The AA similarity criterion shows only that the triangles are the same shape.
3. Similar, △ABC ~ △FED
4. C. RSQ only
5. D. Disagree, by the Triangle Angle Sum Theorem m∠N=55° , so the triangles are similar by the AA similarity criterion.