In Fig. ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ~ ∆ADE, and hence find the lengths of AE and DE.
Solution not provided. Ans. Â AE = 1.07 cm (app.), Â DE = 2.8 cm (app.)
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Short Answer Type
453.DEFG is a square and ∠BAC = 90°. Show that DE2 = BD × EC.
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454.In ∆ABC, if AD is perpendicular to BC. Then, AB2 + CD2 = AC2 + BD2.
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455.In a trapezium ABCD, AC and BD are intersecting at O, AB || DC and AB = 2CD. If area of ∆ABC = 84 cm2, find the area of ∆COD.
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456.∆ABD is a right ∆, right angled at A and AC ⊥ BD. Prove that AB2 = BC. BD.
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457.M is the mid-point of side CD of a parallelogram ABCD. The line BM is drawn intersecting AC and L and AD produced at E. Prove that: EL = 2BL.
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458.In Fig. ST || QR, PS = 2 cm and SQ = 3 cm. What is the ratio of the area of ∆PQR to the area of ∆PST?
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459.In an isosceles triangle ABC with AC = BC. If AB2 = 2AC2, prove ∆ABC is a right triangle.
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Long Answer Type
460.Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.
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