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Ex 8.1, 12 - ABCD is a trapezium in which AB || CD and AD = BC - Ex 8.1

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Ex 8.1, 12 ABCD is a trapezium in which AB ∥ CD and AD = BC . Show that ∠ A = ∠ B [Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E. Given: ABCD is a trapezium where AB ∥ CD and AD = BC To prove: ∠A = ∠B Construction: Extend AB and draw a line through C parallel to DA intersecting AB produced at E Proof: AD ∥ CE & AE ∥ DC In AECD, both pair of opposite sides are parallel, AECD is a parallelogram ∴ AD = CE But AD = BC ⇒ BC = CE So, ∠CEB = ∠CBE From (2) & (3) ∠A = ∠B Hence proved Ex 8.1, 12 ABCD is a trapezium in which AB ∥ CD and AD = BC . Show that (ii) ∠ C = ∠ D From (1) & (2) ∠D = ∠C Hence proved Ex 8.1, 12 ABCD is a trapezium in which AB ∥ CD and AD = BC . Show that (iii) Δ ABC ≅ Δ BAD In ΔABC and ΔBAD, AB = BA ∠B = ∠A BC = AD ∴ ΔABC ≅ ΔBAD Ex 8.1, 12 ABCD is a trapezium in which AB ∥ CD and AD = BC . Show that (iv) diagonal AC = diagonal BD In the last part we proved that ΔABC ≅ ΔBAD ∴ AC = BD  

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