Download Bell Ringers - December 2 1. AD bisects ∠BAC. Find x. B D 2. Solve

December 2, 2010
Bell Ringers - December2 2 2
2. Solve x + 12 = 169
1. AD bisects ∠BAC. Find x.
3. The legs of a right ∆ measure 15 ft
and 20 ft. Find the length of the
hypotenuse.
D
B
(3x + 7.5)º
(5x - 32.5)º
A
16
M
C
Q
O
N
14
17
R
3y - 4
S
15
5x - 3
P
In the diagram, the perpendicular
bisectors of ΔMNP meet at point O
and are shown dashed. Find the
indicated measure.
4. Find NP.
5. Find OP.
6. Find the value of x.
7. Find the value of y.
December 2, 2010
5.3 Use Angle Bisectors of a Triangle
angle bisector : a ray that divides an angle into two congruent
adjacent angles.
distance from a point to a line : the length of the perpendicular
segment from the point to the line
P
Thm 5.5 Angle Bisector Theorem
-If a point is on the bisector of an angle,
then it is__________________ from the sides of the angle.
-If AD bisects ∠BAC and DB ⊥ AB
and DC ⊥ AC, then
B
D
A
C
Thm 5.6Converse of the Angle Bisector Theorem
If a point is in the interior of an angle and is equidistant
from the sides of the angle, then
it lies ______________________________
1
December 2, 2010
D
Ex 1: Find the measure of ∠BAD.
18
18
B
54º
A
Ex 2: Find the value of x. State the theorem used in
each problem.
a.
(3x + 5)º
(4x - 6)º
b.
5x
6x - 5
C
December 2, 2010
Thm 5.7 Concurrency of Angle Bisectors of a Triangle
-The ∠bisectors of a triangle intersect at a point that is
equidistant from the side of the triangle.
B
PD = PE = PF
F
P
A
C
E
Incenter: the point of concurrency of the angle bisectors of
a triangle
Ex 3: The ∠bisectors of ∆XYZ meet at M. Find MK.
X
L
M
Z
8
5
J
K
Y
D