Question

1. complete the proof. given: ad is the perpendicular bisector of bc and bd = 3x + 2 and dc = 4x - 5. prove: x = 7. 1. ad is the perpendicular bisector of bc 2. bd = dc 3. bd = 3x + 2 and dc = 4x - 5 4. 3x + 2 = 4x - 5 5. subtraction property of equality 6. 7 = x 7.

Explanation:

Step1: Use the property of perpendicular bisector

Since \(AD\) is the perpendicular bisector of \(BC\) and \(BD = DC\), and \(BD=3x + 2\), \(DC = 4x-5\).

Step2: Set up the equation

We can set up the equation \(3x + 2=4x - 5\) because \(BD = DC\).

Step3: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(3x+2-3x=4x - 5-3x\), which gives \(2=x - 5\).
Then add 5 to both sides: \(2 + 5=x-5 + 5\), so \(x=7\).

Answer:

\(x = 7\)