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) ABC BAD
In ABC and BAD,
AB = BA
B = A
BC = AD
ABC BAD
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 ABC BAD
AC = BD

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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