Exercise 5 Page 306

According to the Converse of the Perpendicular Bisector Theorem, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

In the diagram, D is equidistant from the endpoints of AC. This and the fact that DB and AC are perpendicular, mean that DB is the perpendicular bisector of AC. Therefore, we can say that AB=BC. With this, we can write an equation to find x. AB=BC ⇒ 5x=4x+3 Let's subtract 4x on both sides to find the value of x.

5x=4x+3

SubEqn

LHS-4x=RHS-4x

x=3

Finally, to find the value of AB, we will substitute 3 for x in the expression 5x.

AB=5x

Substitute

x= 3

AB=5( 3)

Multiply

Multiply

AB=15