The AA, SSS and SAS criteria for similarity. Then the ratio of the areas of similar triangles, and the Pythagoras theorem and its converse proved by similar triangles.
3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson
Created by StemPy LabTwo triangles are similar when their angles are equal and their sides are in the same ratio. Three short tests, AA, SSS and SAS, prove it with far fewer facts. Once two triangles are similar, a length that cannot be measured follows from a ratio.
The areas of two similar triangles are in the ratio of the squares of their corresponding sides. Doubling every side makes the area four times as big, and tripling it makes the area nine times as big. The same square rule holds for corresponding altitudes.
In a right triangle the square on the hypotenuse equals the sum of the squares on the other two sides. The proof uses similar triangles. The converse also holds: if three sides satisfy the rule, the triangle has a right angle. Together they solve distance problems and test for right angles.
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