Transcript Warm-up

Warm-up
1. Draw AB and AC , where A, B, and C are
non-collinear.
2. What do we name this geometric figure?
Angles and Angle Measures
Day 1
What kind of angles do you see in the two blankets?
Section 2.1
Rays
• Part of a line that starts at an endpoint and
extends forever in one direction
• To name a ray, use its endpoint and any
other point on the ray
A
D
H
Slides 8 - 13
An angle is formed by 2 non-collinear rays
that have a common end point.
The rays are the sides of the angle.
The common endpoint is the vertex.
A
You can name the angle in the figure
to the right:
angle ABC or  ABC
angle CBA or  CBA
angle B or  B
angle 1 or 1
1
B
C
Example 1: Angles Naming
3
BAC
CAB
A
3
The set of all points between the sides of the
angle is the interior of an angle. The exterior
of an angle is the set of all points outside the
angle.
Angle Name:
Slides 14- 23
The measure of an angle is the smallest
amount of rotation about the vertex from
one ray to another, measured in degrees.
The geometry tool used to measure an angle is
a protractor.
What type of angle is
used to shoot the pool
ball in to the hole?
Angles - Measurement
How do you
measure an
angle?
1. Place the center mark
of the protractor on the
vertex.
2. Line up the 0 mark with
one side of the angle.
3. Read the measure on
the protractor scale.
Example 2: Measuring and Classifying Angles
Find the measure of each angle. Then classify
each as acute, right, or obtuse.
A. WXV
B. ZXW
Slides 30- 32
Congruent angles are angles that have the same
measure.
Arc marks are used to show that the two angles are
congruent.
Slides 14 - 16
An angle bisector is a ray that divides an angle
into two congruent angles.
JK bisects LJM; thus LJK  KJM.
Example:
Example 3
KM bisects JKL, mJKM = (4x + 6)°, and
mMKL = (7x – 12)°. Find mJKM.
Example 4
OB bisects AOC, mAOB = (3x + 16)°, and
mBOC = (8x – 14)°. Find mAOB.
O
C
B
A
Example 5:
BD bisects ABC, mABD = (6x + 4)°, and
mDBC = (8x – 4)°. Find mABD.
Slides 33 - 36
Example:
m  DAC + m  CAB = m  DAB. So, m  DAB = 35° + 30° = 65°.
Example 6:
In the diagram, 1 is congruent to  2. Use the
information below to find the value of x.
m  1 = x + 12, m  3 = 6x – 4
Example 7:
BD bisects ABC, mABD = (5x - 3)°, and
mDBC = (3x + 15)°. Find mABC.
Review:
1. When do you set the angle measures
equal to solve for the variable?
2. Do the order of the letters matter when
you name an angle? Why or why not?
3. Do the lengths of the sides of an angle
affect its measure?