Similar — Grade 8 Math, what it means and where it is taught
Same shape, possibly different size. Written △ ABC ∼ △ DEF.
Taught in Grade 8 Math.
Where it is taught
What uses it later
This idea is needed for:
- AA similarity — Two pairs of congruent angles prove two triangles similar.
Practise this idea
9 questions in the course bank use Similar, in Dilations & Similarity, Similarity & Proportionality. The first 8 are below; the rest are in those units.
Problem 1
Two similar triangles have areas 9 cm2 and 81 cm2. Find the scale factor between them.
Worked answer
3
k2 = 819 = 9
k = 3
Problem 2
A 6-foot person casts a 4-foot shadow. At the same moment a tree casts a 22-foot shadow. How tall is the tree?
Worked answer
33
heightshadow is the same for both
64 = h22
h = 6 × 224 = 33 feet
Problem 3
Two pairs of congruent angles prove two triangles
- similar
- congruent
- isosceles
- right-angled
Worked answer
similar
The third angle follows, so all three match.
Same shape, any size: similar.
Problem 4
A 5 ft person casts a 4 ft shadow. A tree casts a 32 ft shadow. Find the tree height.
Worked answer
40
54 = h32
h = 40 ft
Problem 5
Similar pentagons have sides 6 and 15. The smaller has area 48. Find the larger area.
Worked answer
300
k = 2.5, k2 = 6.25
48 × 6.25 = 300
Problem 6
Two similar triangles have areas 9 and 81. Find the ratio of their sides.
Worked answer
1:3
k2 = 9
k = 3, so sides are 1:3
Problem 7
Two similar solids have sides in ratio 1:2. Find the ratio of their volumes.
Worked answer
1:8
k3 = 8
Ratio 1:8
Problem 8
Similar triangles have scale factor 3. The smaller has perimeter 14. Find the larger perimeter.
Worked answer
42
14 × 3 = 42