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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.

652 Views

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.

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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.

201 Views

245.
In the given fig, AB || DC. Find the value of x.

Since the diagonals of a trapezium divide each other proportionality.
∴

AO over OC equals BO over OD

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9 straight x minus 57 space equals space straight x squared minus 8 straight x plus 15

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straight x squared minus 17 straight x plus 72 equals 0

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left parenthesis straight x minus 8 right parenthesis space left parenthesis straight x minus 9 right parenthesis space equals space 0

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straight x minus 8 equals 0 space space or space straight x minus 9 equals 0

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space space space space space space straight x equals 8 space space or space space straight x space equals space 9.

1047 Views

246.

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

2955 Views

247.

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

82 Views

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.

1489 Views

Short Answer Type

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

403 Views

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

162 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

Long Answer Type

Short Answer Type

245.
In the given fig, AB || DC. Find the value of x.