Triangles: similarity
Similar triangles, the basic proportionality theorem and Pythagoras.
Learn with Kutty
Go one screen at a time. Press Next when you are ready. Tap 🔊 Read to me to listen.
Similar triangles have the same shape, just a different size.
Look: Every side of the big triangle is 2 times the small one.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1Sides 3, 4, 5 and 9, 12, 15: similar?
2A 2 m stick casts 3 m shadow. A tree casts 18 m. Height?
3Scale 2: area grows how many times?
! Careful!
✗Matching the wrong sides.
✓Match sides opposite equal angles.
✗Thinking area grows by the same scale.
✓Area grows by the scale squared (6 × 6 = 36).
See the whole lesson on one page
Similar triangles have the same shape, just a different size.
If two angles match, the triangles are similar. Then all the sides grow by the same scale. That lets you find heights you cannot reach.
Think of it like thisA photo and its enlargement: same picture, bigger. Every length grows by the same amount.
Solved together
A 1.5 m girl casts a 2 m shadow. A pole casts a 12 m shadow at the same time. How tall is the pole?
Same sun, so same angles: the triangles are similar.
The shadow grew 6 times (2 → 12). So the height grows 6 times too.
1.5 × 6 = 9
AnswerThe pole is 9 m tall.
Now practise it
Kanakku makes new questions on triangles: similarity every time. It shows the working and gives a hint when you are stuck.