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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 64 Page 748

Create a drawing and label the segments.

8

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. 6y-14=10-2y Let's use inverse operations to solve for the variable.

6y-14=10-2y

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Solve for y

LHS+2y=RHS+2y

8y-14=10

LHS+14=RHS+14

8y=24

.LHS /8.=.RHS /8.

y=3

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

AB=6y-14

y= 3

AB=6( 3)-14

Multiply

AB=18-14

Subtract terms

AB=4

Both segments have a length of 4. Using the betweenness of points, we know that the entire segment AC is 4* 2 = 8.

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Exercises p.745-748