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Question

In ∆ABC, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:

(i) ∆OMA ∼ ∆OLC
(ii) OAOC=OMOL

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Solution


i. In OMA and OLC,AOM = COL Vertically opposite anglesOMA = OLC 90° eachOMA ~ OLC AA similarityii. Since OMA ~ OLC by AA similarity, thenOMOL = OAOC = MALC Corresponding sides of similar triangles are proportionalOAOC = OMOL

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