Last updated at Dec. 8, 2016 by Teachoo

Transcript

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.