Question

find the missing length indicated.

1. find cd
2. find df

(image of triangle xyz with segment cd, side xz is 16, markings indicating midpoints or congruent segments)

Explanation:

Step1: Identify Midline Theorem

In triangle \( XYZ \), \( D \) is the midpoint of \( ZY \) (since \( ZD = DY \)) and \( C \) is the midpoint of \( XY \) (since \( XC = CY \)). 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 \( CD \parallel XZ \) and \( CD=\frac{1}{2}XZ \).

Step2: Calculate \( CD \)

Given \( XZ = 16 \), substitute into the formula from Step 1: \( CD=\frac{1}{2}\times16 = 8 \).

Answer:

\( 8 \)