Similar polygons and the AA postulate
Answers are for parents and teachers.
1
PQRS ~ WXYZ with PQ = 9, QR = 12, RS = 15, SP = 6 and WX = 6. Find the other sides of WXYZ and its perimeter.
k = 9/6 = 3/2. XY = 12 ÷ 3/2 = 8, YZ = 15 ÷ 3/2 = 10, ZW = 6 ÷ 3/2 = 4. Perimeter 6 + 8 + 10 + 4 = 28 (and 42 ÷ 3/2 = 28 ✓).
2
Are a 4 × 7 rectangle and an 8 × 12 rectangle similar?
4/8 = 1/2 but 7/12 ≠ 1/2, so they are not similar.
3
In △ABC, ∠A = 35° and ∠B = 70°. In △DEF, ∠D = 70° and ∠F = 75°. Write the similarity with the letters in the right order.
∠C = 75° and ∠E = 35°. Matching: A→E, B→D, C→F, so △ABC ~ △EDF.
4
In △ABC, D is on AB, E on AC, DE ∥ BC, AD = 6, DB = 2, DE = 9 and AE = 9. Find BC and AC.
AB = 8, AD/AB = 6/8 = 3/4. BC = 9 ÷ 3/4 = 12 and AC = 9 ÷ 3/4 = 12.
5
A boy 1.8 m tall casts a 2.4 m shadow. At the same moment a lamp post casts an 8 m shadow. Find the height of the post.
h/8 = 1.8/2.4 = 3/4, so h = 6 m.