Question

If c and d are the midpoints of AB and AC respectively then prove that AD=1/4 AB.

Answer 1

AC = CB (as C is the mid-point of line segment AB)

Add AC to both sides, we get

AC + AC = AC + CB ( Axiom 2: If equals are added to equals, then the wholes are equal)

So, 2 AC = AB (as AC+CB = AB)

AC = AB/2 ........ (1)

Next, AD = DC (as D is the mid-point of AC)

Add AD to both sides, we get

AD + AD = AD + DC (Axiom 2; same as above)

2 AD = AC (as AD + DC = AC)

Therefore, AD = AC/2 ......... (2)

Substituting value of AC from (1) in (2), we get

AD = AB/2÷ 2

AD = AB/2 x 1/2

AD = 1/4 AB