Understand similar triangles, the basic proportionality theorem, and apply similarity to maps and scale models.
Triangles are similar (AA, SSS, or SAS similarity) if their corresponding angles are equal and sides are proportional.
Triangle ABC has angles 50°, 60°, 70°. Triangle DEF has angles 50°, 60°, 70°. Are they similar?
Yes, by AA similarity (equal corresponding angles)
Two triangles have sides in ratio 2:3 for all corresponding sides. Are they similar?
Yes, by SSS similarity
Similarity applies directly to maps and scale models — real distances and model distances are proportional.
A map has scale 1:100,000. If two cities are 5 cm apart on the map, find the actual distance.
5×100,000=500,000 cm=5 km
A model car is built at 1:20 scale. If the model is 22 cm long, find the actual car's length.
22×20=440 cm=4.4 m
1. Two triangles have angles 45°,65°,70° and 45°,65°,70°. Are they similar?
2. Two similar triangles have a side ratio of 3:5. If the smaller triangle's side is 9 cm, find the corresponding side of the larger triangle.
3. A map has scale 1:50,000. Two towns are 8 cm apart on the map. Find the actual distance.
4. A model building is built at 1:200 scale, and is 15 cm tall. Find the actual building's height.
5. Two similar triangles have areas in ratio 4:9. Find the ratio of their corresponding sides.