The AA and SAS similarity tests
Answers are for parents and teachers.
1
DE ∥ BC with D on AB and E on AC; AD = 5, DB = 10, DE = 8. How long is BC?
24
2
One triangle has sides 4 and 7 cm with a 50° angle between them; another has 12 and 21 cm with a 50° angle between them. Are they similar? Find k.
Yes, since 12/4 = 21/7 = 3; k = 3.
3
An upright 2 m pole casts a 1 m shadow. At the same time a building casts a 15 m shadow. How tall is the building (m)?
30
4
△ABC ∽ △A₁B₁C₁ with k = 4 and S(ABC) = 3 cm². What is S(A₁B₁C₁) (cm²)?
48
5
Why is the AA test the most convenient for checking similarity?
Only two angles need comparing and no sides have to be measured.