Question

AB bisects CD at point M, CD bisects AB at point M, and AB = 4 x CM. Describe the relationship between AM and CD

Answer 1

$\text{Given that AB bisects the line segment CD at the point M,}\\ \text{And CD bisects the line segment AB at the point M. so M is the }\\ \text{midpoint of both the line segements AB and CD.}\\ \\ \text{also we have given a relation that, }AB=4\times CM\\ \text{and we need to find a relation between AM and CD.}\\ \\ \text{observe that since M is the midpoint of CD, so we have }CD=2\times CM\\ \\ \Rightarrow CM=\frac{CD}{2}$

$\text{and M is midpoint of AB, so }AB=2\times AM\\ \\ \text{so with these substitutions, the given realtion gives}\\ \\ AB=4\times CM\\ \\ \Rightarrow 2\times AM=4\times \frac{CD}{2}\\ \\ \Rightarrow 2\times AM=2\times CD\\ \\ \Rightarrow AM=CD$

Hence the relationship between AM and CD is : AM=CD