Transcript Complaining - Ms. Kilgard

Obj. 5 Measuring Angles
Objectives:
• Correctly name an angle
• Identify acute, right, obtuse, and straight angles
• Set up and solve linear equations using the Angle
Addition Postulate and angle bisector properties
• Use a protractor to measure and draw angles
• Construct a congruent angle and angle bisector
angle
A figure formed by two rays or sides
with a common endpoint.
C
●
Example:
A●
●
R
vertex
The common endpoint of two rays or
sides (plural vertices).
Example: A is the vertex of the above
angle
Notation: An angle is named one of
three different ways:
T
●
1
●
1.
●
E
A
By the vertex and a point on each
ray (vertex must be in the middle) :
TEA or AET
2. By its vertex (if only one angle): E
3. By a number: 1
Example
Which name is not correct for the angle
below?
●R
S
●
2
●
TRS
SRT
RST
2
R
T
Measuring Angles
1. Draw a ray on your paper about 3“ long.
2. Draw another ray about 3“ long connected to it,
creating an acute angle. Label the vertex A.
3. Line the center mark of your protractor at the vertex
and the 0º/180º marking along one side (different
protractors use different methods of alignment).
4. Count up from 0º to where the other side crosses
the protractor’s edge. That number is the measure
of angle A.
obtuse angle
Angle whose measure is greater than
90˚ and less than 180˚
right angle
Angle whose measure is exactly 90˚
acute angle
Angle whose measure is less than 90˚
straight angle Angle whose measure is exactly 180˚
(a straight line)
According to these definitions, did you
draw an acute angle?
Constructing a Congruent Angle
1. Draw an acute angle. Label the vertex I.
2. Draw a ray at least 3“ long and label the endpoint H.
3. Place the point of your compass at point I and draw
an arc that intersects both sides of I. Label the
intersection points W and N.
4. Using the same compass setting, place the point
of the compass on point H and draw an arc that
intersects the ray. Label the intersection point S.
5. Place the point of the compass at point N and draw
an arc that intersects with the point W. Without
changing the compass setting, put the point of the
compass at point S and draw an arc that intersects
the first arc. Label the intersection point L.
6. Connect H and L. The angle should be the same as
I.
congruent
angles
Angles that have the same measure.
L●
W
●
●
N
●I
H●
●
S
mWIN = mLHS
WIN  LHS
Notation: “Arc marks” indicate
congruent angles.
Notation: To write the measure of an
angle, put a lowercase “m” in front of
the angle bracket.
mWIN is read “measure of angle
WIN”
interior of an
angle
The set of all points between the sides
of an angle
Angle
Addition
Postulate
If D is in the interior of ABC, then
mABD + mDBC = mABC
(part + part = whole)
●
●
A
D
●
●
B
C
angle
bisector
A ray that divides an angle into two
congruent angles.
S●
Example:
F
●
U●
●
N
UF bisects SUN; thus SUF  FUN
or mSUF =
mFUN
Constructing an Angle Bisector
1. Draw an angle with sides at least 3“ long and label
the vertex J
2. Open the compass about 2“.
3. Place the point of the compass on point J and draw
an arc that intersects both sides. Label the
intersection points K and L.
4. Place the compass point on K and draw an arc in
the interior of the angle. Repeat on point L. Label
the intersection point M.
5. Connect J and M. This is an angle bisector.
Drawing a Specific Angle
1. Draw a ray at least 3“ long. Label the endpoint B.
2. Line the center mark of your protractor at the
endpoint and the 0º/180º mark along the ray.
3. Count up from 0º along the edge of the protractor
until you find 55º degrees. Make a mark on your
paper at that point.
4. Remove the protractor and connect the endpoint of
the ray with the mark.