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Mathematics : Triangles

Short Answer Type

361. In the figure, ∆ABC ~ ∆PQR. Also area of (∆ABC) = 4 area of (∆PQR). If BC = 12 cm, find QR.

522 Views

Long Answer Type

362. In the given Fig.

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and MN || BC. Prove that: ∆AMN ~ ∆ABC.

64 Views

363. In triangle PQR, MN is drawn parallel to QR.

(i) If

space space PM equals 1 half PQ space then space find space fraction numerator ar left parenthesis increment PMN right parenthesis over denominator ar left parenthesis increment PQR right parenthesis end fraction.

(ii) If

MN space equals space 1 third QR semicolon space find space fraction numerator ar left parenthesis increment PQR right parenthesis over denominator ar left parenthesis increment PMN right parenthesis end fraction.

122 Views

Short Answer Type

364.

In the given Fig. PB and QA are perpendi-cular t to segment AB, if PO = 4 cm, QO = 7 cm and ar (∆POB) = 80 cm², find ar (∆QOA).

109 Views

Long Answer Type

365. In the given Fig. ∆AOD ~ BOC if AD = 10 cm, BC = 5 cm, AO = 6.5 cm and OC = 2.8 cm. Find OD and OB. Also find

fraction numerator ar left parenthesis increment AOD right parenthesis over denominator ar left parenthesis increment BOC right parenthesis end fraction.

80 Views

Short Answer Type

366. In the Fig. find PR and PQ, when QR = 26 cm, PO = 6 cm and OR = 8 cm.

230 Views

367. ABC is a right triangle right angled at C. Let BC = a, CA = b, AB = c and let p be the length of perpendicular from C on AB, prove that
(i) cp = ab
(ii)

1 over straight p squared equals 1 over straight a squared plus 1 over straight b squared.

239 Views

Long Answer Type

368. If a line is drawn parallel to one side of a triangle, the other two sides are divided in the same ratio, Prove. Use this result to prove the following.
In the given figure, if ABCD is a trapezium in which AB || DC || EF, then

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79 Views

369. In a right angled triangle, the square of hypotenuse is equal to the sum of the squares of the two sides. Given that ∠B of ∆ABC is an acute angle and AD ⊥ BC.
Prove that AC² = AB² + BC² - 2 BC . BD.

80 Views

370. State and Prove Pythagoras theorem, use the theorem and calculate area (∆PMR) from the given figure.

166 Views