5. Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third
side (Using converse of basic proportionality theorem)
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EXPLANATION.
GIVEN.
in ∆ ABC
=> D and E are the mid point of the sides AB
and AC.
TO PROVE.
=> DE || BC
PROOF.
=> AD = DB ...(1)
=> AE = EC .....(2)
=> AD / DB = 1 .....(3)
=> AE / EC = 1 .....(4)
From equation (3) and (4) we get,
=> AD / DB = AE / EC
THEREFORE,
=> DE || BC
By using the converse of basic proportionality
theorem.
HENCE PROVED.
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Answer:
If a line divides any two sides of a triangle in the same ratio then the line must parallel to the third side. Given: ΔABC in which D and E are the mid points of AB and AC respectively such that AD=BD and AE=EC. Hence , the line joining the mid points of any two sides of a triangle is parallel to the third side...
Step-by-step explanation:
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