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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Inscribed Angles

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Exercise 63 Page 748

Create a drawing and label the segments.

54

Practice makes perfect

Let's start by illustrating AC and its midpoint B.

A midpoint divides a segment into two equal parts. This means AB and BC are congruent. Therefore, we can equate the expressions. 4x-5=11+2x Let's use inverse operations to solve for the variable.

4x-5=11+2x

▼

Solve for x

LHS-2x=RHS-2x

2x-5=11

LHS+5=RHS+5

2x=16

.LHS /2.=.RHS /2.

x=8

We can now substitute the value of x into either expression to find the lengths of AB and BC.

AB=4x-5

x= 8

AB=4( 8)-5

Multiply

AB=32-5

Subtract terms

AB=27

Both segments have a length of 27. Using the betweenness of points, we know that the entire segment AC is 27* 2 = 54.

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Exercises p.745-748