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Triangles

Short Answer Type

241. In Fig. DE || BC and

space AD over DB equals 3 over 5.

If AC = 4.8 cm, find the length of AE.

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

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243.
In the given fig., $PS over SQ equals PT over TR$ and ∠PST = ∠PRQ. Prove that ∆PQR is an isosceles triangle.

We have,

PS over SQ equals PT over TR

rightwards double arrow

ST parallel to QR

[Using converse of Basic proportionality theorem]
⇒    ∠PST = ∠PQR
[Corresponding angles]
⇒    ∠PRQ = ∠PQR
[∵ ∠PST = ∠PRQ (given)]
⇒    PQ = PR
[∵ Sides opposite to equal angles are equally]
⇒ ∆PQR is isosceles.

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244.

In the given fig, ∆ABD is a right triangle, right angled at A and AC ⊥ BD. Prove that AB² = BC. BD.

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245.

In the given fig, AB || DC. Find the value of x.

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246.

In the given fig, express x in terms of a, b and c.

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247.

In the given fig, $OA over OC equals OD over OB.$ Prove that ∠A = ∠C and ∠B = ∠D.

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Long Answer Type

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

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Short Answer Type

249. In a ∠ABC, BD and CE are the altitudes. Prove that ∠ADB and ∠AEC are similar. Is ∆CDB ~ ∆BEC?

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250. The perimeters of two similar triangles ABC and PQR are respectively 36 cm and 24 cm. If PQ = 10 cm, find AB.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

243. In the given fig., and ∠PST = ∠PRQ. Prove that ∆PQR is an isosceles triangle.

Long Answer Type

Short Answer Type

243.
In the given fig., $PS over SQ equals PT over TR$ and ∠PST = ∠PRQ. Prove that ∆PQR is an isosceles triangle.