Transcript 1.4 Angles and Their Measures

1.6 Angles
and Their
Measures
Angle
• An angle consists of two
different rays that have
the same endpoint. The
rays are the sides of the
angle. The initial point is
the vertex of the angle.
• The angle that has sides
AB and AC is denoted by
BAC, CAB, A. The
point A is the vertex of the
angle.
C
Sides
A
B
Vertex
Ex.1: Naming Angles
P
• Name the angles in
the figure:
S
SOLUTION:
Q
There are three
different angles.
R
• PQS or SQP
You should not name any of
• SQR or RQS
these angles as Q because
• PQR or RQP
all three angles have Q as their
vertex. The name Q would
not distinguish one angle from
the others.
Note:
• The measure of A is denoted by mA.
The measure of an angle can be
approximated using a protractor, using
units called degrees(°).
• For instance, BAC
has a measure of
B
50°, which can be
written as
mBAC = 50°.
A
C
more . . .
• Angles that have the same
measure are called congruent
angles.
Note – Equal & Congruent are
not exactly the same!!!
MEASURES ARE EQUAL
ANGLES ARE CONGRUENT
mBAC = mDEF
BAC  DEF
“is equal to”
“is congruent to”
Classifying Angles
• Angles are classified as acute, right, obtuse,
and straight, according to their measures.
Angles have measures greater than 0° and less
than or equal to 180°.
Interior/Exterior
• A point is in the
interior of an angle if
it is between points
that lie on each side
of the angle.
• A point is in the
exterior of an angle if
it is not on the angle
or in its interior.
E
A
D
Postulate 6: Angle Addition
Postulate
• If P is in the interior
of RST, then
mRSP + mPST =
mRST
R
P
S
T