☰ Year plan · Mathematics

Similarity of triangles

Week 8 · Similarity of triangles: the AA, SSS and SAS cases, right triangles and real heights · 3 lessons
Answers are for parents and teachers.
1
△ABC has ∠A = 80°, ∠B = 40°; △DEF has ∠D = 80°, ∠F = 60°. Are they similar? Which vertices match?
2
In △ABC, DE ∥ BC with AD = 5, DB = 3, AC = 12 and DE = 10. Find AE and BC.
3
Are the triangles with sides 7, 9, 12 and 14, 18, 24 similar? Find k.
4
In a right triangle the altitude to the hypotenuse cuts it into BD = 4 and DC = 9. Find the altitude AD and the hypotenuse BC.
5
A 2 m pole has a shadow 1.5 m long. At the same time a tower’s shadow is 36 m. How tall is the tower?