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Triangles

Short Answer Type

441. In figure. DB ⊥ BC, DE ⊥ AB and AC ⊥ BC Prove that

BE over DE equals AC over BC

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442. In figure, DE || AC and

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Prove that DC || AP.

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443. In ∆ABC, if AD is the median so that: AB² + AC² = 2 (AD² + BD²).

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444. If the areas of two similar triangles are equal. Prove that they are congruent.

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445. In figure, PQ || BC and AP : PB = 1:2, Find

space space space fraction numerator ar left parenthesis increment APQ right parenthesis over denominator ar left parenthesis increment ABC right parenthesis end fraction.

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446. In figure AB || DE and BC || EF. Prove that AC || DF.

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447. In figure AD ⊥ BC. Prove that AB² + CD² = BD² + AC².

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Long Answer Type

448. E is a point on the side AD produced of a ||^gm ABCD and BE intersects CD at F. Show that ∆ABE ~ ∆CFB.

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449. In ∆ABC, ∠A is acute. BD and CE are perpendiculars on AC and AB respectively. Prove that AB × AE = AC × AD.

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450. The diagonals of a trapezium ABCD, with AB $parallel to$ DC, intersects each other at the point O. If AB = 2CD. Find the ratio of the areas of ∆COD.

Solution not provided.
Ans. 4:1

92 Views