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161. In the given figure, if OA = OB, OD = OC, then ∆AOD ≅ ∆BOC by congruency rule

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162. If ∆ABC, is right angled at B, then:

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163. In the figure below, ABCD is a square and P is the mid point of AD. BP and CP are joined. Prove that ∠PCB = ∠PBC.

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164. ∆ABC is an isosceles triangle with AB = AC, D and E are the points on BC such that BE = CD. Prove that ∆ABD ≅ ∆ACE.

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165. In the given figure, ABC is a triangle in which AB = AC and AD is an altitude on BC. Prove that AD bisects CA.

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166.

In the figure given below, PQR is a triangle and S is any point in its interior, show that SQ + SR < PQ + PR.

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167. In the given figure, the diagonal AC of a quadrilateral ABCD bisects the angles A and C. Prove that AB = AD and CB = CD.

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168. In the given figure, AB = CF, EF = BD and ∠AFE = ∠CBD. Prove that (i) ∆AFE ≅ ∆CBD and (ii) AE = CD

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169. ∆ABC is isosceles triangle in which AB = AC, P and Q are points on AB and AC such that AP = AQ. Prove that ∠ABQ = ∠ACP.

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Solution not provided.

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