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Triangles

Short Answer Type

451. In Fig. ∠L = ∠M - 46°. Express x in terms of a, b and c where a, b, c are lengths LM, MN and NK respectively.

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Long Answer Type

452.

In Fig. ∆ABC is right angled at C and DE ⊥ AB. Prove that ∆ABC ~ ∆ADE, and hence find the lengths of AE and DE.

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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.

Solution not provided.

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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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