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

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.