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Last updated at Sept. 24, 2018 by Teachoo

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Example 1 - Chapter 7 Class 9 - Triangles In Fig. , OA = OB and OD = OC. Show that (i) ∆ AOD ≅ ∆ BOC Given: OA = OB ...(1) and OD = OC ...(2) To prove: ΔAOD ≅ ΔBOC Proof: Line CD & AB intersect. ∠ AOD = ∠ BOC (Vertically opposite angles) ...(3) In ∆ AOD and ∆ BOC, OA = OB (From (1)) ∠ AOD = ∠ BOC (From (3)) OD = OC (From (2)) So, Δ AOD ≅ Δ BOC (SAS Congruence Rule) Example 1 In Fig. , OA = OB and OD = OC. Show that (ii) AD ∥ BC. Δ AOD ≅ Δ BOC (From 1st part) ∠ OAD = ∠ OBC (CPCT) But ∠ OAD & ∠ OBC and these form a pair of alternate angles If a transversal intersects two lines such that pair of alternate interior angles is equal, then lines are parallel. Therefore, AD ∥ BC.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.