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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 1 Page 434

Use the Perpendicular Bisector Theorem.

29

We are given the following diagram and asked to find the length of AB. Let's consider the given diagram.

As we can see, 5x-11 represents the length of AB. Therefore, to find AB, we need first to calculate the value of x.

Finding x

From the diagram, we see that AC intersects BD at the midpoint C. Moreover, it is perpendicular to BD. Thereby, AC is a perpendicular bisector of BD. Let's use the Perpendicular Bisector Theorem.

Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

By this theorem, A is equidistant from the endpoints of BD. This means that AB and AD have the same measures. From the diagram, we know that the length of AB is 5x-11 and the length of AD is 3x+5. Let's set these expressions equal. 5x-11= 3x+5 Now, we can solve this equation for x.

5x-11=3x+5

▼

Solve for x

LHS-3x=RHS-3x

2x-11=5

LHS+11=RHS+11

2x=16

.LHS /2.=.RHS /2.

x=8

Finding AB

Now that we know the value of x, we can evaluate the expression 5x-11 and find the length of AB.

AB=5x-11

x= 8

AB=5( 8)-11

Multiply

AB=40-11

Subtract term

AB=29

The length of AB is 29.