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In ( ABC ), let (D ), (E ), and (F ) be the midpoints of (AB ), (BC ), and (CA )…
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
, let
D
D
D
,
E
E
E
, and
F
F
F
be the midpoints of
A
B
AB
A
B
,
B
C
BC
B
C
, and
C
A
CA
C
A
respectively. (a) Prove that quadrilateral
D
E
C
F
DECF
D
E
C
F
is a parallelogram. (b) Show that
△
D
E
F
\triangle DEF
△
D
E
F
is similar to
△
A
B
C
\triangle ABC
△
A
B
C
and find the ratio of their areas.
Related theory
Areas of Similar Triangles
Similarity
Similarity of Triangles
Quadrilaterals
Triangle similarity conditions
Triangles
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