In the Fig, DE || AB and FE || DB. Prove that DC2 = CF . AC.

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Triangles

Short Answer Type

431.

In the Fig. ∠ABD = ∠CDB = ∠PQB = 90°. If AB = x units, CD = y units and PQ = z units, that $1 over straight x plus 1 over straight y equals 1 over straight z.$

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432.
In the Fig, DE || AB and FE || DB. Prove that DC² = CF . AC.

Solution not provided.

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Long Answer Type

433. P and Q are points on sides CA and CB respectively of triangle ABC. right angled at C. Prove that AQ² + BP² = AB² + +PQ²

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Short Answer Type

434.

In the given fig, PQ = 24 cm, QR 26 cm, ∠PAR = 90°, PA = 6 cm and AR = 8 cm. Find ∠QPR.

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435.

In figure, P and Q are points on the sides AB and AC respectively at ∆ABC such that AP = 3.5 cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm find BC.

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436. If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium given.

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Long Answer Type

437. Two ∆s ABC and DBC are on the same base BC and on the same side of BC in which ∠A = ∠D = 90°. If CA and BD meet each other at E, show that AE.EC = BE.ED

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438. In ∆ABC, XY is parallel to BC and it divides ∆ABC into two parts of equal area.Prove that

BX over AB equals space fraction numerator square root of 2 minus 1 over denominator square root of 2 end fraction.

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Short Answer Type

439. D, E and F are the mid-points of the sides AB, BC and CA respectively of ∆ABC. Find

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Long Answer Type

440. D and E are points on the sides CA and CB respectively of ∆ABC right angled at C. Prove that AE² + BD² = AB² + DE²

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