Question

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

Explanation:

Step1: Identify Midline 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 Midline Theorem (also known as 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 midline, and \(BE=\frac{1}{2}CD\).

Step2: Solve for \(CD\)

We know \(BE = 22\). From the Midline Theorem, \(BE=\frac{1}{2}CD\), so we can solve for \(CD\) by multiplying both sides by 2:
\(CD = 2\times BE\)
Substitute \(BE = 22\) into the formula:
\(CD = 2\times22 = 44\)

Answer:

B. \(CD = 44\)