Question

1. ac=24, ab=bc, and ac=cd. bc = __ bd = __

Explanation:

Step1: Find BC

Given \( AC = 24 \) and \( AB = BC \), so \( AB + BC = AC \). Let \( AB = BC = x \), then \( x + x = 24 \), which simplifies to \( 2x = 24 \). Solving for \( x \), we divide both sides by 2: \( x=\frac{24}{2}=12 \). So \( BC = 12 \).

Step2: Find CD

Given \( AC = CD \) and \( AC = 24 \), so \( CD = 24 \).

Step3: Find BD

To find \( BD \), we add \( BC \) and \( CD \). So \( BD = BC + CD \). Substituting the values of \( BC = 12 \) and \( CD = 24 \), we get \( BD = 12 + 24 = 36 \).

Answer:

\( BC = 12 \), \( BD = 36 \)