Question

what is the value of cd?
a) cd = 22
b) cd = 44
c) cd = 33
d) cd = 11

Explanation:

Step1: Identify Midsegment Theorem

In triangle \(ACD\), \(B\) is the midpoint of \(AC\) (since \(AB = BC\)) and \(E\) is the midpoint of \(AD\) (since \(AE = ED\)). By the Midsegment Theorem, the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length. So, \(BE\) is the midsegment, meaning \(BE=\frac{1}{2}CD\).

Step2: Solve for \(CD\)

Given \(BE = 22\), from the midsegment theorem: \(22=\frac{1}{2}CD\). Multiply both sides by 2: \(CD = 22\times2 = 44\).

Answer:

B. \(CD = 44\)