5.3 Use Angle Bisectors of Triangles
5.3
Bell Thinger
1. AD bisects
ANSWER

BAC. Find x.
20

2. Solve x² + 12² = 169.
ANSW...
5.3
Example 1
5.3
Find the measure of GFJ.

SOLUTION
Because JG FG and JH FH and
JG = JH = 7, FJ bisects GFH by the
Converse...
Example 2
5.3
SOCCER A soccer goalie’s position relative to the ball
and goalposts forms congruent angles, as shown. Will
...
Example 2
5.3
SOLUTION
The congruent angles tell you that the goalie is on
the bisector of LBR. By the Angle Bisector
Theo...
Example 3
5.3
ALGEBRA For what value of x does
P lie on the bisector of A?
SOLUTION
From the Converse of the Angle
Bisect...
Guided Practice
5.3
In Exercises 1–3, find the value of x.
1.

ANSWER

15
Guided Practice
5.3
In Exercises 1–3, find the value of x.
2.

ANSWER

11
Guided Practice
5.3
In Exercises 1–3, find the value of x.
3.

ANSWER

5
5.3
5.3
Example 4
5.3
In the diagram, N is the incenter of

ABC. Find ND.

SOLUTION
By the Concurrency of Angle Bisectors of a Tri...
Example 4
5.3
c 2 = a 2 + b2
2

2

20 = NF + 16
2

Pythagorean Theorem
2

400 = NF + 256

144 = NF
12 = NF

2

Substitute ...
Exit Slip
5.3
Find the value of x.
1.

ANSWER 12
Exit Slip
5.3
Find the value of x.
2.

ANSWER 20
Exit Slip
5.3
3. Point D is the incenter of XYZ. Find DB.

ANSWER 10
5.3

Homework
Pg 327-330
#14, 19, 20, 24, 29
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5.3 use angle bisectors of triangles

  1. 1. 5.3 Use Angle Bisectors of Triangles 5.3 Bell Thinger 1. AD bisects ANSWER BAC. Find x. 20 2. Solve x² + 12² = 169. ANSWER ±5 3. The legs of a right triangle measure 15 feet and 20 feet. Find the length of the hypotenuse. ANSWER 25 ft
  2. 2. 5.3
  3. 3. Example 1 5.3 Find the measure of GFJ. SOLUTION Because JG FG and JH FH and JG = JH = 7, FJ bisects GFH by the Converse of the Angle Bisector Theorem. So, mGFJ = mHFJ = 42 .
  4. 4. Example 2 5.3 SOCCER A soccer goalie’s position relative to the ball and goalposts forms congruent angles, as shown. Will the goalie have to move farther to block a shot toward the right goalpost R or the left goalpost L?
  5. 5. Example 2 5.3 SOLUTION The congruent angles tell you that the goalie is on the bisector of LBR. By the Angle Bisector Theorem, the goalie is equidistant from BR and BL . So, the goalie must move the same distance to block either shot.
  6. 6. Example 3 5.3 ALGEBRA For what value of x does P lie on the bisector of A? SOLUTION From the Converse of the Angle Bisector Theorem, you know that P lies on the bisector of A if P is equidistant from the sides of A, so when BP = CP. BP = CP x + 3 = 2x –1 4=x Set segment lengths equal. Substitute expressions for segment lengths. Solve for x. Point P lies on the bisector of A when x = 4.
  7. 7. Guided Practice 5.3 In Exercises 1–3, find the value of x. 1. ANSWER 15
  8. 8. Guided Practice 5.3 In Exercises 1–3, find the value of x. 2. ANSWER 11
  9. 9. Guided Practice 5.3 In Exercises 1–3, find the value of x. 3. ANSWER 5
  10. 10. 5.3
  11. 11. 5.3
  12. 12. Example 4 5.3 In the diagram, N is the incenter of ABC. Find ND. SOLUTION By the Concurrency of Angle Bisectors of a Triangle Theorem, the incenter N is equidistant from the sides of ABC. So, to find ND, you can find NF in NAF. Use the Pythagorean Theorem stated on page 18.
  13. 13. Example 4 5.3 c 2 = a 2 + b2 2 2 20 = NF + 16 2 Pythagorean Theorem 2 400 = NF + 256 144 = NF 12 = NF 2 Substitute known values. Multiply. Subtract 256 from each side. Take the positive square root of each side. Because NF = ND, ND = 12.
  14. 14. Exit Slip 5.3 Find the value of x. 1. ANSWER 12
  15. 15. Exit Slip 5.3 Find the value of x. 2. ANSWER 20
  16. 16. Exit Slip 5.3 3. Point D is the incenter of XYZ. Find DB. ANSWER 10
  17. 17. 5.3 Homework Pg 327-330 #14, 19, 20, 24, 29
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