Question

in a figure p is the midpoint of a b and d is the midpoint of AC prove that ad is equal to one fourth of CD​

Answer 1

Question:

I guess this is your question: If AB is a line and C is the mid-point of AB and D is mid-point of AC then prove that AD=¼AB

Solution:

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

Add AC to both sides, we get

AC + AC = AC + CB ( 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 (If equals are added to equals, the wholes are equal)

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 ½

AD = ¼AB

Thus, proven

Hope you've understood!

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