Download angle

MIDPOINT QUIZ
Find the coordinate of the midpoint of the segment with ear
of endpoints.
(2, 3)
1.(6, 1), (-2, 5)
2.(-5, 4), (-6, 3)
(-5.5, 3.5)
3.(4, 3), (-1, 6)
(1.5, 4.5)
4.(4, -3), (5, 5)
(4.5, 1)
5.One endpoint of a segment is (12, -8). The midpoint is
(3, 18). Find the coordinates of the other endpoint>
(-6, 44)
POOLROOM MATH
OBJECTIVES
• Learn to show the measurement of angles and segments
on figures.
• Practice using the tools of measurement (protractor and
ruler)
• Become familiar with the symbols for making figures.
• Learn the idea of congruence of angles.
• Learn that in physical situations the incoming angle is
equal in measure to the outgoing angle.
INTRODUCTION
• Angles can defined named and
measured.
P
• You can use the terms that you
defined in the first lesson to write a
precise definition of an angle.
• An angle is formed by two rays that
T
share a common endpoint, provided
that the two rays are noncollinear.
• The common endpoint of the two
rays is called the vertex of the angle.
A
The two rays are the sides also
called arms of the angle.
• You can name the angle in the figure below as “TAP” or
“PAT” or use the angle symbol and write TAPor PAT.
ANGLES
P
• Notice that the vertex must be the
middle letter and the first and last
letters each name a point on a
different ray.
• Since there are no other angles with
vertex A, you can also simply call
this A .
T
A
EXAMPLE
Name all the angles in these
drawings.
SOLUTION:
DEFINITIONS
• The measure of an angle is the smallest amount of
rotation about the vertex from one ray to the other
measured in degrees.
• The measure of an angle can be any value between 0°
and 180°.
• The largest amount of rotation less than 360° between
the two rays is called the reflex measure of an angle.
MEASURING ANGLES
• The geometry too you use to measure an angle is called
a protractor.
GROUP WORK
• Use your protractor to measure the angles as accurately
as you can.
CLASSIFYING ANGLES
• Which angles measure more than 90°?
• Two angles are congruent if and only if they have equal
measures.
• You use identical markings (tick marks) to show that two
angles in a figure are congruent.
ANGLE BISECTOR
• A ray is the angle bisector if it
contains the vertex and divides
the angle into two congruent
angles.
• In the angle BCA, CD bisects it
into two congruent angles
ACD and DCB
GROUP INVESTIGATION
Use your protractor to study these shots.
Step 1: use your
protractor to find the
measure of angle 1.
which is the correct
outgoing angle? Which
point A or B will the ball
hit.
Step 2: which point on the cushion, W, X, or Y should the
white ball hit so that the outgoing angle passes through the
center of the 8-ball?
Step 3: Compare your results with your group members’
results. Does everyone agree?
GROUP INVESTIGATION
Step 4: How would you
hit the white ball against
the cushion so that the
ball passes over the
same spot on the way
back?
Step 5: How would you hit the ball so that it bounces off
three different points on the cushions without ever touching
cushion CP?
Ch. 1.2 Concept Practice
• Virtual Pool Investigation
• CP 1.2 #1-17