Question

Using converse of Basic Proportionality theorem, prove that line segment joining
midpoints of two sides of triangle is half of the third side.​

Answer 1

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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Answer 2

Answer:

Answer

Given:

ΔABC in which D and E are the mid-points of sides AB and AC respectively.

To prove: DE∥BC

Proof:

Since, D and E are the mid-points of AB and AC respectively

∴AD=DB and AE=EC

⇒

DB

AD

=1 and

EC

AE

=1

⇒

DB

AD

=

EC

AE

Therefore, by the converse of Basic proportionality Theorem

DE∥BC