Given AC = BC, prove that AC = 1/2 AB, assuming A, C, and B are collinear with C between A and B.

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution to the problem:

The problem states:

This problem assumes that A, C, and B are collinear points, and C lies between A and B on a straight line segment.

Understand the relationship between the line segments.
If point C lies between points A and B on a straight line, then the length of the entire segment AB is the sum of the lengths of the segments AC and CB.
$AB = AC + CB$
Use the given information.
We are given that $AC = BC$ .
Substitute the given information into the equation from Step 1.
Replace $CB$ with $AC$ in the equation $AB = AC + CB$ :
$AB = AC + AC$ $AB = 2AC$
Solve for AC.
To express AC in terms of AB, divide both sides of the equation by 2:
$AC = \frac{1}{2} AB$
This proves the required statement.

Answer