Similar Figures Properties

Pre-Algebra · Axiom Academy

Same shape, different size: similar figures keep every corresponding angle equal and scale every corresponding side by one shared factor. Watch a small triangle grow into a larger copy. Every side stretches by the same factor and the corner angles never change — so the two triangles have the same shape , just at a different size. That is what the symbol records. 2. Property 1: Corresponding Angles Are Equal The animation lights up each pair of corresponding angles — angles in the same position in each triangle. No matter how much bigger the copy is, each matched pair measures exactly the same. Scaling stretches lengths; it leaves angles untouched. 3. Property 2: Corresponding Sides Are Proportional Now the animation measures each pair of corresponding sides and forms its ratio. Watch the punchline: all three ratios come out to the same number . That single number is the scale factor k — the one amount every side was multiplied by. If has sides 3, 4, 5 and has sides 6, 8, 10 , then . Every side of is twice as long, so the scale factor is k = 2 . 4. Putting It Together: One Copy Lands on the Other Here is why the two properties always travel together. The animation rotates the small triangle and then scales it up by the factor k — and it drops exactly onto the large one. The match is perfect only because the angles already agree and a single scale factor fixes every side at once. This also gives you two ways to test for similarity, and you only need one of them:

This is the written version of the interactive lesson above. See the full Pre-Algebra course.