Question

use the figure below to find the measure of \overline{bc}.

Explanation:

Step1: Identify Midline Theorem

The segments \( AB' \) and \( B'B \) are congruent (marked with one tick), and \( AC' \) and \( C'C \) are congruent (marked with two ticks). So \( B' \) is the midpoint of \( AB \), and \( C' \) is the midpoint of \( AC \). By the Midline Theorem (also called the Midsegment Theorem) in a triangle, the segment connecting the midpoints of two sides is parallel to the third side and half its length.

Step2: Apply Midline Theorem

In triangle \( ABC \), \( B'C' \) connects the midpoints of \( AB \) and \( AC \). The length of \( BC \) is \( 72 \) cm. By the Midline Theorem, \( B'C'=\frac{1}{2}BC \).

Step3: Calculate \( B'C' \)

Substitute \( BC = 72 \) cm into the formula: \( B'C'=\frac{1}{2}\times72 = 36 \) cm.

Answer:

\( 36 \) cm