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Triangles

Long Answer Type

251.

In the given Fig, two triangles ABC and DBC lie on the same side of base BC. P is a point on BC such that PQ || BA and PR || BD. Prove that: QR || AD.

3069 Views

Short Answer Type

252.

In the given fig, if ∠P = ∠RTS. Prove that ∆RPQ ~ ∆RTS.

108 Views

253. In a ∆ABC, DE || BC, if

DE equals 2 over 3 BC

and area of ∆ABC = 81 cm². Find the area of ∆ADE.

429 Views

254.

In the given fig, ST || QR, PS = 2 cm and SQ = 3 cm. What is the ratio of the area of ∆PQR to the area of ∆PST?

146 Views

255. Prove that the diagonals of a rectangle bisect each other and are equal.

In ∆AOB and ∆COD, we have
∠AOB = ∠COD
[Vertically opposite angles]
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Therefore by using Using AA similar condition, we have
$space space increment AOB tilde increment COD$

$rightwards double arrow$ $AO over OC equals BO over OD equals AB over DC$

$rightwards double arrow$ $1 half equals 5 over DC space left square bracket because space AB space equals space 5 space cm right square bracket$

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75 Views

256.

In the given Fig. PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 cm² find the area of ∆QOA.

1171 Views

257. In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio 4 : 9, find the ratio of the areas of ∆ABC and ∆PQR.

826 Views

258. In ∆ABC shown in Fig, DE || BC. If BC = 8 cm, DE = 6 cm and area of ∆ADE = 45 cm², what is the area of ∆ABC.

515 Views

Long Answer Type

259. If D is a point on the side AB of ∆ABC such that AD : DB = 3:2 and E is a point on BC such that DE || AC ; find the ratio of the areas of ∆ABC and ∆BDE.

381 Views

Short Answer Type

260.

In the given fig, DE is parallel to BC and AD = 1 cm, BD = 2 cm. What is the ratio of the area of ∆ABC to the area of ∆ADE?

3119 Views