Using Theorem 2.2, prove that the line joining the mid-points of any t

1.	Using Theorem 2.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.
Answer» In ∆ABC, D and E are mid-points of AB and AC. ∴ AD = DB AE = EC AB = 2AD AC = 2AE \(\frac{AD}{AB} = \frac{AE}{AC}\) = \(\frac{1}{2}\) As per S.S.S. Postulate. ∆ADE ~ ∆ABC ∴ They are equiangular triangles. ∴ ∠A is common. ∠ADE = ∠ABC ∠ADE = ∠ACE These are pair of corresponding angles ∴ DE \|\| BC

Using Theorem 2.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Answer»

In ∆ABC, D and E are mid-points of AB and AC.

∴ AD = DB

AE = EC

AB = 2AD

AC = 2AE

\(\frac{AD}{AB} = \frac{AE}{AC}\) = \(\frac{1}{2}\)

As per S.S.S. Postulate.

∆ADE ~ ∆ABC

∴ They are equiangular triangles.

∴ ∠A is common.

∠ADE = ∠ABC

∠ADE = ∠ACE

These are pair of corresponding angles

∴ DE || BC