Thales’ theorem and its use
Answers are for parents and teachers.
1
A 28 cm segment is divided in the ratio 3 : 4. How long is the larger part (cm)?
16
2
Parallel lines cut the sides of an angle: OA = 4 cm, AB = 6 cm, OC = 10 cm. How long is CD (cm), given OA : AB = OC : CD?
15
3
Two sides of a triangle are 14 cm and 21 cm and the third is 25 cm. When the bisector of the angle between the first two divides the third side, how long is the smaller part (cm)?
10
4
a = 6 cm, b = 9 cm, c = 8 cm. How long is d (cm) if a : b = c : d?
12
5
Write step by step how to divide a segment into 4 equal parts.
1) draw a ray from A; 2) lay 4 equal segments on it; 3) join the last point to B; 4) draw lines parallel to it through the other points.