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Triangles

Long Answer Type

181. In the adjacent figure, if LM || CB and LN || CD, prove that

AM over AB equals AN over AD

177 Views

182. In the given figure. DE || AC and DF || AE. Prove that

BF over FE equals BE over EC.

149 Views

183. In the given Fig. DE || OQ and DF || OR. Show that EF || QR.

299 Views

184. In the given fig, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

220 Views

Short Answer Type

185. Prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

436 Views

186. Using Theorem 6.2 (N.C.E.R.T.), prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Given a ∆ABC, in which DE is a line which intersects AB and AC in D and E respectively, such that AD = DB and AE = EC

To Prove : DE || BC
Proof: We have.

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rightwards double arrow

AD over DB equals 1

...(i)
Also, AE = EC

rightwards double arrow

AE over EC equals 1

...(ii)
Comparing (i) and (ii), we get

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Therefore, by using converse of Basic proportionality theorem, we have
DE || BC.

684 Views

Long Answer Type

187. ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that

AO over BO equals CO over DO.

231 Views

188. The diagonals of a quadrilateral ABCD intersect each other at point O such that

AO over BO equals CO over DO.

Show that ABCD is a trapezium.

454 Views

189. State which pairs of triangles in the given Fig, are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:

108 Views

Short Answer Type

190.

In the given fig. ∆ODC ~ ∆OBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.

450 Views