This document contains 6 math problems involving similar triangles, similar figures, and proportional relationships: 1) Calculate lengths and determine similarity between two triangles, 2) Find values for x given similar cones, 3) Identify similar triangles in a trapezium and find values of x and y, 4) Find values of x and y given two similar triangles, 5) Name corresponding sides and find values of x and y for two similar figures, 6) Find values of x and y.

1. a
b
24 30
8
8
4
15
Student’s Task 7
1. Calculate the length of a and b.
2. State, with reasons, whether ΔABC is similar to ΔPQR and find the value of x.
3. The figure shows two similar cones.
a. Find the value of x.
b. What is the ratio of the base circumference of the smaller cone to that of the big
cone?
4. ABCD is a trapezium where AB is parallel to DC. Name a pair of similar triangles. If
AM = 5 cm, MC = 7 cm, BM = 6 cm, AB = 8 cm, DC = x cm and MD = y cm, find the
values of x and y.

2. 5. In the figure, ΔABC is similar to ΔPQR. Given that AB = 8 cm, AC = 10 cm, PQ =12
cm, QR = 9 cm, BC = x cm and PR = y cm, calculate the values of x and y.
6. PQRS is similar to ABCD.
a. Name three pairs of corresponding sides.
b. Find the values of x and y.