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Standard IX
Mathematics
A Parallelogram and a Triangle between the Same Parallels
Question 12 i...
Question
Question 12 (iii)
ABCD is a trapezium in which AB | | CD and AD =BC (see the given figure). Show that
Δ
A
B
C
≅
Δ
B
A
D
.
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Solution
In
Δ
A
B
C
and
Δ
A
B
D
,
AB=BA
(Common side)
BC=AD
(Given)
∠
B
=
∠
A
(Proved before)
Δ
A
B
C
≅
Δ
A
B
D
(SAS congruence rule).
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Similar questions
Q.
ABCD is a trapezium in which AB | | CD and AD =BC (see the given figure). Show that
Δ
A
B
C
≅
Δ
B
A
D
.
Q.
Question 12 (ii)
ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Show that
∠
C
=
∠
D
.
Q.
Question 12 (i)
ABCD is a trapezium in which AB
parallel
CD and AD =BC (see the given figure). Show that
∠
A
=
∠
B
.
Q.
A
B
C
D
is a trapezium in which
A
B
∥
C
D
and
A
D
=
B
C
(See figure). Show that
(i)
∠
A
=
∠
B
(ii)
∠
C
=
∠
D
(iii)
△
A
B
C
≅
Δ
B
A
D
Q.
Question 12 (iv)
ABCD is a trapezium in which AB || CD and AD =BC (see the given figure). Show that
Diagonal AC=diagonal BD.
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A Parallelogram and a Triangle between the Same Parallels
Standard IX Mathematics
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