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1.2 & 1.3 Classifying Angles
2.5 Angle Relationships
Measure and classify angles.Identify and use congruent angles and the bisector of an angle.Discover relationships between special pair of angles.
VocabularyDegree, ray, angle, sides, vertex, interior, exterior, right angle, acute angle, obtuse angle, angle bisector. Adjacent angles, linear pair angles, vertical angles, supplementary angles & complementary angles
What is an Angle?
Two rays that share the same endpoint
.
Bvertex
BC side
BA side
ABC, CBA
B, 4
4
Name all angles that have B as a vertex.
Answer: 5, 6, 7, and ABG
a. Name all angles that have X as a vertex.
b. Name the sides of 3.
c. Write another name for 3.
Answer: 1, 2, 3, and RXBor RXN
Answer: AXB, AXN, NXA, BXA
Answer:
Degrees: Measuring Angles
We measure the size of an angle using
degrees.
Here are some examples of angles and
their degree measurements.
Measuring angle
To measure an angle ,we use a protractor
geogebra
D
G
F
BA
E
An angle divides a plane into two parts. Points
A, D, and E lie on the angle.
Points C and B lie in the interior of the angle.
Points F and G lie in the exterior of the
angle.
C B
F
B
Names of Angles
Type of angle Description
Acute Angle an angle that is less than 90°
Right Angle an angle that is 90° exactly
Obtuse Anglean angle that is greater than 90°
but less than 180°
Straight Angle an angle that is 180° exactly
Reflex Angle an angle that is greater than 180°
Classify TYV as right, acute, or obtuse.
TYV is marked with a right angle symbol, so measuring is not necessary.
Answer:is a right angle.
Measure each angle named and classify it as right, acute, or obtuse.
a. CZD
b. CZE
c. DZX
Answer: 150, obtuse
Answer: 90, right
Answer: 30, acute
Angle Bisector
An angle bisector is a ray that divides
an angle into two equal angles.
Examples
Angles that have the same measure are
congruent angles.
Q
M
P R
N
025
025
QMPNMP
SIGNS A railroad crossing sign forms congruent angles. In the figure, WVX ZVY. If mWVX 7a + 13and mZVY 10a – 20, find the actual measurements of WVX and ZVY.
Answer:
Adjacent angles are two angles that lie in the
same plane, have a common vertex, and a
common side, but no common interior points.
A
CB
D
A
CB
D
AC
B
D
Examples
Non example
Determine whether the following statement can be assumed from the figure below. Explain.
VYW and TYS are adjacent angles.
Answer: No; they do not share a common side.
Vertical angles are angles opposite to one
another at the intersection of two lines.
(vertical angles are congruent)
E C
B
D
A
CB
D
ExamplesNon example
A
E
Name two acute vertical angles.
There are four acute angles shown. There is one pair of vertical angles.
Answer: The acute vertical angles are VZY and XZW.
A Linear pair is a pair of adjacent angles
whose noncommon sides are opposite rays
A
CB
D
Example No example
A
C
B D
B,D, and C are no collinear
Name an angle pair that satisfies each condition.
a. two acute vertical angles
b.two adjacent angles whose sum is less than 90
Answer: BAC and CAD or EAF and FAN
Answer: BAC and FAE,CAD and NAF, or BAD and NAE
Supplementary angles:
Two angles that add up to 180°
A
CB∠BDA and ∠ADC
are supplementary
AB
D
0100 080∠A and ∠B
are supplementary
Determine whether the following statement can be assumed from the figure below. Explain.
TYW and TYU are supplementary.
Answer: Yes; they form a linear pair of angles.
ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the other angle.
Explore You know that the sum of the measures of supplementary angles is 180.
Plan Draw two figures to represent the angles.
Let the measure of one angle be x.
Solve
Answer: 31, 149
ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the other angle.
Complementary angles:
Two angles that add up to 90°
ZR
P Q
2
∠1 and ∠2 are
complementary∠PQR and ∠XYZ are
complementary
YX0401 050
Find the measure of each letter angle
ALGEBRA Find the measures of two
complementary angles if one angle
measures six degrees less than five
times the measure of the other.
Answer: 16, 74
The little symbol ("corner") is used
to indicate a right angle.
is read perpendicular to
C
B D
A
Perpendicular lines meet to form right angles
AD ┴ BC
ALGEBRA: Find x so that .
If , then mKJH 90. To find x, use KJI and IJH.
Substitution
Add.
Subtract 6 from each side.
Divide each side by 12.
Answer:
Sum of parts whole
Answer:
ALGEBRA Find X and Y so that
are perpendicular.
Determine whether each statement can be assumed from the figure below. Explain.a.
b. TAU and UAY are
complementary.
c. UAX and UXA are adjacent.
Answer: Yes; lines TY and SX are perpendicular.
Answer: No; they do not share a common side.
Answer: No; the sum of the two angles is 180, not 90.
Homework
Workbook 1.2 , 1.3, & 2.5
