Point 6 of 10 — Unit 2: Similarity of Polygons and Triangles, Areas and Circle TheoremsQuestion bank: 0 questions (0 with pictures)
06 2-6 The right triangle and Euclid's theorems
In right triangle ABC, right-angled at A, with altitude AD drawn to the hypotenuse BC, the two smaller triangles are similar to each other and to the whole triangle.
The two theorems
Leg theorem: the square of a leg equals the hypotenuse times the projection of that leg on the hypotenuse: AB² = BD × BC and AC² = CD × BC.
Altitude theorem: the square of the altitude to the hypotenuse equals the product of the two projections: AD² = BD × DC.
Useful deductions
AB/AC = √(BD/DC); sin and cos of the acute angles read directly from the projections.
BD + DC = BC, so the two projections add to the hypotenuse.
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