Basic Concept Of Similarity Of Triangle
Similar triangles
Two triangles are similar when one is just an enlarged or shrunk copy of the other — same angles, same shape, sides scaled by one fixed number. Drag the shapes below and watch the proof happen in real time.
Drag a corner
Move any corner of the solid triangle. The dashed triangle always keeps the exact same shape — it’s the solid one, stretched out from corner A.
Find the tree’s height
You can’t measure a tall tree with a tape measure — but you can measure shadows. The sun’s rays hit the ground at the same angle everywhere at the same moment, so the person and the tree stand in two similar right triangles.
AA — Angle, Angle
Two angles of one triangle match two angles of the other. The third pair has to match too, since angles in a triangle always add to 180°. That alone proves similarity.
SAS — Side, Angle, Side
Two pairs of sides are in the same ratio, and the angle trapped between them matches. That fixes the whole triangle’s shape.
SSS — Side, Side, Side
All three pairs of sides are in the same ratio to each other. No angles need checking — matching ratios all the way round is enough.
Similarity of Triangles Simulation & Quiz
Similarity Detective — Case Files
You’re the detective on the Triangle Beat. Every case shows you a pair of shapes and a handful of clues — angles, sides, or shadow lengths. Study the evidence, decide whether the shapes are truly similar, name the rule that proves it, and close the case by working out the missing measurement.