Question

1. according to the perpendicular bisector conjecture, in triangle $\triangle abc$, if segment $ad$ is the perpendicular bisector of side $bc$, and $bc$ measures 20 units, what are the measures of segments $bd$ and $cd$?

a. $bd = 8$ units, $cd = 12$ units
b. $bd = 10$ units, $cd = 10$ units
c. $bd = 9$ units, $cd = 11$ units
d. $bd = 11$ units, $cd = 9$ units

Explanation:

Step1: Recall Perpendicular Bisector Conjecture

The Perpendicular Bisector Conjecture states that if a segment is the perpendicular bisector of another segment, then it divides the second segment into two equal parts. So, \( BD = CD \) and \( BD + CD = BC \).

Step2: Set Up Equation

Given \( BC = 20 \) units and \( BD = CD \) (from the conjecture), let \( BD = CD = x \). Then \( x + x = 20 \), which simplifies to \( 2x = 20 \).

Step3: Solve for \( x \)

Divide both sides of \( 2x = 20 \) by 2: \( x=\frac{20}{2}=10 \). So \( BD = 10 \) units and \( CD = 10 \) units.

Answer:

b. \( BD = 10 \) units, \( CD = 10 \) units