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In parallelogram
MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles
Problem
In parallelogram
A
B
C
D
ABCD
A
B
C
D
, diagonal
A
C
AC
A
C
is drawn. The point
E
E
E
is the midpoint of
A
C
AC
A
C
. Segments
B
E
BE
B
E
and
D
E
DE
D
E
are joined. (a) Prove that
△
A
B
C
\triangle ABC
△
A
B
C
is congruent to
△
C
D
A
\triangle CDA
△
C
D
A
. (b) Show that
△
A
B
E
\triangle ABE
△
A
B
E
is congruent to
△
C
D
E
\triangle CDE
△
C
D
E
. (c) Deduce that
B
E
=
D
E
BE = DE
B
E
=
D
E
and
∠
A
B
E
=
∠
C
D
E
\angle ABE = \angle CDE
∠
A
B
E
=
∠
C
D
E
.
Related theory
Quadrilaterals
Triangle Congruence
Triangle Congruence Criteria
Similarity
Triangles
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