Theorem 6.7 : If a perpendicular is drawn from
the vertex of the right angle of a right triangle to
the hypotenuse then triangles on both sides of
the perpendicular are similar to the whole triangle
and to each other.
arom in proving the
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△ABC right angled at B and ⊥ from B intersecting AC at D(BD⊥AC)In△ADB&△ABC∠A=∠A(common)∠ADB=∠ABC{ Each 90 ∘ } △ADB∼△ABC{ By AA Similarity criterion} -(1)Similarly,In△BDC&△ABC∠C=∠C{ common}∠BDC=∠ABC{ Each 90 ∘ } △BDC∼△ABC{ By AA Similarity Criterion} -(2)from(1)&(2)△ADB∼△ABC&△BDC∼△ABC If one △le is similar to another △le,and second△le is similar, to the third △le,then first & third △le are similar.△ADB∼△BDC
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abc it's Avery simple
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