Question

Section (D) Long Answer Type 2Q* 5M = 10 Marks
No 8. AB and CD are respectively the smallest and longest sides of quadrilateral
ABCD. Show that 2A > 2C and 2B > ZD​

Answer 1

Answer:

Given: AB and C are respectively the smallest and longest sides of quadrilateral ABCD.

Join A and C and B and D and mark angle

In ΔABC,

BC>AC

∴∠1=∠2...............................(1) (angle opposite to the longer side is greater)

In ΔADC,

CD>AD

∴∠3=∠4 ................................(2) (angle opposite to the longer side is greater)

Add (1) and (2) we get

∠1+∠3>∠2+∠4

∴∠A>∠C

In ΔABD,

AD>AB

∴∠5=∠6...............................(3) (angle opposite to the longer side is greater)

In ΔADC,

CD>AD

∴∠7=∠8 ................................(4) (angle opposite to the longer side is greater)

Add (3) and (4) we get

∠5+∠7>∠6+∠8

∴∠B>∠D

solution

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