342.In the given Fig. PM is median of triangle PQR is the mid-point of PM and MN || QS. Prove that: PS = SN = NR.
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343.The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, find the corresponding side of the second triangle.
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344.Two poles of height a metres and b metres are p metres apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by
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345.Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in 1 and AD produced to E. Prove that EL = 2 BL.
347.ABCD is a trapezium in which AB is parallel to DC. If AC and BD intersect at E and triangle AED is similar to triangle BEC. Prove that AD = BC.
Solution not provided.
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Short Answer Type
348.
In the given Fig. ∠CAB = 90° and AD is perpendicular to BC. If AC = 15 cm, AB = 20 cm and BD = 16 cm, find AD.
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Long Answer Type
349.In the given Fig; ∠EBA = ∠CDA = 90°, BC = 12 cm, CD = 18 cm, CE = (3x - 2) cm and AC = (4x + 2) cm. Show that ∆ECB is similar to ∆ACD. Hence, find the lengths of segments CE and AC.
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350.In ∆ABC, AD ⊥ BC and BE ⊥ AC. Prove: (i) ∆ACD ~ ∆BCE. (ii) AC × CE = BC × CD.
Short Answer Type
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