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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex .8.2, 3 ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. Given: ABCD is rectangle where P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively To prove: PQRS is a rhombus Construction: Join A & C Proof: A rhombus is a parallelogram with all sides equal First we will prove PQRS is a parallelogram, and then prove all sides equal From (1) & (2) PQ ∥ RS and PQ = RS In PQRS, one pair of opposite side is parallel and equal. Hence, PQRS is a parallelogram. Now we prove all sides equal In ∆ APS & ∆ BPQ AP = BP ∠ PAS = ∠ PBQ AS = BQ ∴ ∆ APS ≅ ∆ BPQ ∴ PS = PQ But PS = RQ & PQ = RS ∴ PQ = RS = PS = RQ Hence, all sides are equal Thus, PQRS is a parallelogram with all sides equal So, PQRS is a rhombus Hence proved

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.