D,E,F are the midpoints of the sides BC , CA , AB respectively of triangle ABC. then triangle DEF is congruent to triangle
Answers
Given : D,E,F are the midpoints of the sides BC , CA , AB respectively of triangle ABC
To Find : ΔDEF ≅ ΔAFE ≅ ΔFBD , ≅ ΔEDC
Solution:
Line joining the mid point of two sides of a triangle is half of third side
D is mid point of side BC & E is mid point of side CA
hence DE = AB/2
E is mid point of side CA & F is mid point of AB
=> EF = BC/2
D is mid point of side BC & F is mid point of AB
=> DF = AC/2
=> DE/AB = EF/BC = DF/AC = 1/2
Two triangles having corresponding sides proportional are similar
=> ΔDEF ≈ Δ ABC
ΔDEF & ΔAFE
EF = EF
DE = AF ( DE = AB/2 , AF = AB/2)
DF = AE ( DF = AC/2 , AE = AC/2)
=> ΔDEF ≅ ΔAFE
Similarly ΔDEF ≅ ΔFBD
ΔDEF ≅ ΔEDC
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