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Example 3 - Line-segment AB is parallel to CD. O is - Examples

Example 3 - Chapter 7 Class 9 Triangles - Part 2

 

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Example 3 Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see figure). Show that (i) ∆AOB ≅ ∆DOC (ii) O is also the mid point of BC Given: AB || CD O is the mid-point of AD i.e. OA = OD To prove: (i) ∆AOB ≅ ∆DOC (ii) O is also the mid point of BC i.e. OB = OC Proof: AB || CD and BC is the transversal, ∠ABO = ∠ DCO Also, since lines AD & BC intersect ∠AOB = ∠ DOC Consider ∆ AOB and ∆ DOC. ∠ABO = ∠ DCO ∠AOB = ∠ DOC OA = OD ∴ ∆ AOB ≅ ∆ DOC So, OB = OC Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.