Download 5.3 Angle Bisectors Below is angle ABC. Draw the angle bisector of

5.3 Angle Bisectors
Below is angle ABC.
1. Draw the angle bisector of angle ANG.
2. Label the bisector as ray NB
3. Draw a segment that is perpendicular to ray AN to point B. Find the length.
4. Find the shortest length from point B to ray NG.
5. What is the relationship between the length of the two segments?
A
N
G
Theorem: If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
P is the point of concurrency of the three angle bisectors of the
triangle. P is called the __________________________.
1.
2.
Label the triangle to show the congruent angles.
What is the relationship between the lengths of segment
DP, PE and PF. Why are there right angles by D, E and F?
Label the congruent segments.
Theorem: The incenter of a triangle is equidistant from the sides of the triangle.
Recall!!
M is the circumcenter of triangle ABC. Label all of the congruent
segments and the right angles.
Segment GH is the midsegment of GH. I is the midpoint of AC. Label all of the congruent and parallel parts.
Matching:
A. concurrent lines B. equidistant from the endpoints of the segment
D. circumcenter
E. equidistant from the vertices of the triangle
F. equidistant from the sides of the triangle
G. Incenter
C. point of concurrency
1. The point of concurrency of the angle bisectors of a triangle is named the _?_ .
1.
2. Three or more lines that intersect at the same point are called: ? .
2.
3. The point where 2 or more lines intersect is called the ? .
3.
4. Any point on the perpendicular bisector of a segment is ? .
4.
5. The point of concurrency of the perpendicular bisectors of a triangle is named the ? .
5.
6. The point of concurrency of the perpendicular bisectors of a triangle is ? .
6.
7. The point of concurrency of the angle bisectors of a triangle is _?_ .
7.
Tick mark the following diagrams to show all possible information.
8. Perpendicular Bisector of a Segment
9. Angle Bisector
( CP is the perpendicular bisector)
( AD is the angle bisector)
C
B
D
A
P
A
B
C
10. Perpendicular Bisectors of a Triangle
11. Angle Bisectors of a Triangle
B
B
A
G
A
C
D
E
12. CP is the perpendicular bisector. Find the value of x and y.
C
3y - 12
A
12
9
P
D
F
G
F
C
x
B
E
13. Is point P on the perpendicular
14. AD is the angle bisector.
bisector, BD ? Why?
Find the BD and the m BAD .
A
11
P
12
9
x
6
B
B
D
5
A
D
20°
y+4
C
C
Your turn to try!
16. The perpendicular bisectors of 
RST meet at point D. Find DR.
18. The angle bisectors of TUV
meet at point W. Find the value of D.
U
S
2d + 7
10
X
D
W
Y
8
R
T
16
T
4d – 1 Z
V