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Problems
In quadrilateral
MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles
Problem
In quadrilateral
A
B
C
D
ABCD
A
B
C
D
, the sides satisfy
A
B
=
C
D
AB = CD
A
B
=
C
D
and
B
C
=
A
D
BC = AD
B
C
=
A
D
. Diagonal
A
C
AC
A
C
is drawn. (a) Prove that
△
A
B
C
≅
△
C
D
A
\triangle ABC \cong \triangle CDA
△
A
B
C
≅
△
C
D
A
. (b) Using the result of part (a), show that
∠
A
B
C
=
∠
C
D
A
\angle ABC = \angle CDA
∠
A
B
C
=
∠
C
D
A
. (c) Hence, prove that the diagonal
A
C
AC
A
C
bisects
∠
B
A
D
\angle BAD
∠
B
A
D
and
∠
B
C
D
\angle BCD
∠
B
C
D
.
Related theory
Properties of Triangles
Triangle Properties
Triangle Congruence
Similarity
Triangle Congruence Criteria
Triangles
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