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Mathematics : Triangles

Long Answer Type

301. In ∆ABC, let P and Q he points on AB and AC respectively such that PQ || BC. Prove that the median AD bisects PQ.

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Short Answer Type

302. ABC is a triangle in which AB = AC and D is a point on AC such that BC² = AC × CD. Prove that BD = BC.

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Long Answer Type

303.

In the given Fig, ∠1 = ∠2. Prove that ∆ADE ~ ∆ABC.

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304.

In the given Fig. DEFG is a square and ∠BAC = 90°. Prove that
(i) ∆AGF ~ ∆DBG.
(ii) ∆AGF ~ ∆EFC.
(iii) ∆DBG ~ ∆AEFC
(iv) DE² = BD × EC.

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Short Answer Type

305. The diagonal BD of a parallelogram ABCD intersects AE at a point F, where E is any point on the side BC. Prove DF.EF = FB.FA.

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Long Answer Type

306. Prove that the line segments joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle.

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Short Answer Type

307.

In the given Fig., AC ⊥ BC, BD ⊥ BC and DE ⊥ AB. Prove that ABC ~ BDE.

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Long Answer Type

308. Through (the vertex D of a parallelogram ABCD, a line is drawn to intersect the sides BA and BC produced at E and F respectively. Prove that

DA over AE equals FB over BE equals FC over CD.

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309.

In the given Fig, PA, QB and RC are each perpendicular to AC. Prove that $1 over straight x plus 1 over straight z plus 1 over straight y.$

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310. In ∆ABC, DE is parallel to base BC with D on AB and E on AC. If

space AD over DB equals 2 over 3 comma

find

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