1. Using basic proportionality theorem, prove that a line drawn through the mid point of one side of a triangle parallel to another side bisects the third side.
Proof: Let D is the mid point of AB and DE is parallel to BC.
To prove: E is the mid point of AC.
Proof: Since DE is parallel to BC, therefore by basic proportionality theorem CA x CA = CB x CDCA2 = CB x CD proved
4. ABC is a right angled triangle, right angle at B and BD is perpendicular to AC. If AB = 6, BC = 8 and AC = 10, then BD = ?
C = C
Hence ABC is similar to BDC
So BD = 3.6
5. ABC is a triangle in which DE is parallel to BC. If AD = 4, BD = 3, AE = 12, find the value of AC.
Solution: Since DE is parallel to BC, therefore
x = 9
so AC = 12 + 9 = 21