Download 1.3 Measuring and Constructing Angles.notebook

1.3 Measuring and Constructing Angles.notebook
August 17, 2016
In your Foldable (Angles Section)
An angle ( ) is a figure formed by two rays, or sides,
with a common endpoint called the vertex.
ex
ter
on ior
B
Vertex
A
interior
1
Names for this angle:
BAC
CAB
A*
1
o
exterino
r C
* The one-letter name can only be used if the angle
does not share a vertex with any other angle.
Congruent angles are angles that have the same
measure.
m∠ABC = m∠DEF
∠ABC ≅ ∠DEF
Arc marks are used to show that the two angles are
congruent.
An angle bisector is a ray that divides an angle into
two congruent angles.
JK bisects ∠LJM;
thus ∠LJK ≅ ∠KJM.
1
1.3 Measuring and Constructing Angles.notebook
August 17, 2016
What we will learn today:
~ To name, measure, and classify
angles
~ Apply the properties of congruent
angles and angle bisectors
An angle ( ) is a figure formed by two rays, or sides,
with a common endpoint called the vertex.
ex
ter
on ior
B
Vertex
A
1
interior
Names for this angle:
BAC
CAB
A*
1
o
exterino
r C
* The one-letter name can only be used if the angle
does not share a vertex with any other angle.
Example 1: Naming Angles
A surveyor recorded the angles formed by a transit
(point A) and three distant points, B, C, and D. Name
three of the angles.
B
A
C
D
2
1.3 Measuring and Constructing Angles.notebook
August 17, 2016
Measuring and Classifying Angles
Measure each angle to the nearest degree. Classify
the angles as acute, right, or obtuse.
1.
2.
3.
4.
JHI 40o, acute
IHK 90o, right
JHM 90o, right
MHI 130o, obtuse
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1.3 Measuring and Constructing Angles.notebook
August 17, 2016
Examples: Using the Angle Addition Postulate
(a) If m<DEG = 115°, and m<DEF = 48°.
Find m<FEG.
(b) m<XWZ = 121° and m<XWY = 59°.
Find m<YWZ.
4
1.3 Measuring and Constructing Angles.notebook
August 17, 2016
Congruent angles are angles that have the same
measure.
m∠ABC = m∠DEF
∠ABC ≅ ∠DEF
Arc marks are used to show that the two angles are
congruent.
An angle bisector is a ray that divides an angle into
two congruent angles.
JK bisects ∠LJM;
thus ∠LJK ≅ ∠KJM.
5
1.3 Measuring and Constructing Angles.notebook
August 17, 2016
Examples: Finding the measure of an angle
(a) KM bisects <JKL, m<JKM = (4x + 6)°, and
m<MKL = (7x – 12)°. Find m<JKM.
(b) QS bisects <PQR, m<PQS = (5y -1)°, and
m<PQR = 68°. Find m<PQS.
6