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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Bisectors of Triangles

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Exercise 3 Page 411

Use the Perpendicular Bisector Theorem.

LP=15

Practice makes perfect

We are given the following diagram and asked to find the length of LP.

As we can see, 10x-5 represents the length of LP. Therefore, to find LP, we need first to find the value of x.

Finding x

From the diagram, we see that LN intersects MP at the midpoint N. Also, it is perpendicular to MP. Thereby, LN is the perpendicular bisector of MP. 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, L is equidistant from the endpoints of MP. This means that LM and LP have the same lengths. From the diagram, we know that the length of LM is 7x+1 and the length of LP is 10x-5. Let's set these expressions equal. 7x+1= 10x-5 Now, we can solve this equation for x.

7 x + 1 = 10 x - 5

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Solve for x

LHS-7x=RHS-7x

1 = 3x-5

LHS+5=RHS+5

6=3x

Rearrange equation

3x=6

.LHS /3.=.RHS /3.

x = 2

Finding LP

Now that we know the value of x, we can evaluate the expression 10x-5 and find the length of LP.

10x-5

x= 2

10( 2)-5

Multiply

20-5

Subtract term

15

The length of LP is 15.

Subchapter links

Exercises p.411-415