Download Triangles classified by angles

8-2 Classifying Angles
Warm Up
Problem of the Day
Lesson Presentation
Course 2
8-2 Classifying Angles
Warm Up
1. What percent of the model is shaded?
71%
2. Find the value of 52 + 53.
150
3. What is the percent of change
if 20 is increased to 25?
25%
4. On a scale drawing of a tree with a scale of 1 cm = 0.9 m,
the height of the tree is 1.2 cm. What is the actual height
of the tree?
1.08 m
Course 2
8-2 Classifying Angles
Learn to identify angles and angle pairs.
An angle is formed by two
rays with a common
endpoint. The two rays are
the sides of the angle. The
common endpoint is the
vertex.
A
Vertex
B
1
Angles are measured in degrees (°).
Course 2
C
8-2 Classifying Angles
An angle’s measure determines the type of
angle it is.
A right angle is an angle that
that measures exactly 90°. The
symbol indicates a right angle.
An acute angle is an angle
that measures less than 90°.
An obtuse angle is an angle
that measures more than 90°
but less than180°.
A straight angle is an angle
that measures 180°.
Course 2
8-2 Classifying Angles
Tell whether each angle is acute, right, obtuse
or straight.
A.
obtuse angle
Course 2
B.
acute angle
8-2 Insert
Lesson
Title Here
Classifying
Angles
Tell whether each angle is acute, right,
obtuse, or straight.
A.
straight angle
Course 2
B.
acute angle
8-2 Classifying Angles
If the sum of the measures of two angles is 90°,
then the angles are complementary angles.
If the sum of the measures of two angles is 180°,
then the angles are supplementary angles.
Course 2
8-2 Classifying Angles
Omplementary
upplementary
Course 2
= 90˚
+ 90˚
= 180˚
8-2 Classifying Angles
Reading Math
A•
B•
1
•
C
You can name this angle ABC,
CBA, B, or 1.
Course 2
8-2 Classifying Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
OMP and PMQ
P
Q
O
M
Since 60° + 30° = 90°, PMQ and OMP are
complementary.
Course 2
8-2 Classifying Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
NMO and OMR
Reading Math
Read mNMO as
“the measure of
angle NMO.”
O
N
M
Since 15° + 165° = 180°, NMO and OMR are
supplementary.
Course 2
R
8-2 Classifying Angles
Use the diagram to tell whether the angles are
complementary, supplementary, or neither.
PMQ and QMR
P
Q
M
R
Since 30° + 75° = 105°, PMQ and QMR are neither
complementary or supplementary.
Course 2
8-2 Classifying Angles
Angles A and B are complementary.
If mA is 56°, what is the mB?
Angles P and Q are supplementary.
If mP is 32°, what is the mQ?
Course 2
8-6 Classifying Triangles
Learn to classify triangles by their side lengths
and angle measures.
One way to classify triangles is by the lengths of
their sides.
Course 2
8-6 Classifying Triangles
Triangles classified by sides
A scalene triangle
has no congruent sides.
Course 2
8-6 Classifying Triangles
Triangles classified by sides
An isosceles triangle
has 2 congruent sides
Course 2
8-6 Classifying Triangles
Triangles classified by sides
In an equilateral triangle, all of the
sides are congruent.
Course 2
8-6 Classifying Triangles
Another way to classify triangles is by the measures
of their angles.
Triangles classified by angles
In an acute triangle, all of the
angles are acute.
Course 2
8-6 Classifying Triangles
Triangles classified by angles
An obtuse triangle has
one obtuse angle.
Course 2
8-6 Classifying Triangles
Triangles classified by angles
A right triangle
has one right angle.
Course 2
8-6 Classifying Triangles
Classify each triangle according to its sides
and angles.
A. isosceles Two congruent sides
acute
Three acute angles
This is an isosceles acute triangle.
B. scalene
right
No congruent sides
One right angle
This is a scalene right triangle.
Course 2
8-6 Classifying Triangles
Classify each triangle according to its sides
and angles.
C. equilateral Three congruent sides
acute
Three acute angles
This is an equilateral acute triangle.
D. scalene
obtuse
No congruent sides
One obtuse angle (exceeds 90°)
This is a scalene obtuse triangle.
Course 2
8-6 Insert
Lesson
Title Here
Classifying
Triangles
Classify each triangle according to its sides
and angles.
E. isosceles Two congruent sides
obtuse
One obtuse angle
This is an isosceles obtuse triangle.
F. isosceles
right
Two congruent sides
One right angle
This is an isosceles right triangle.
Course 2
8-6 Classifying Triangles
Identify the different types of triangles in the
figure, and determine how many of each there are.
Course 2
Type
How many
Name
Scalene
2
ABD,
BCD
Isosceles
2
ACE,
ABC
Right
ABD,
BCD
Obtuse
2
1
Acute
1
ACE
ABC
8-6 Insert
Lesson
Title Here
Classifying
Triangles
Identify the different types of triangles in the
figure, and determine how many of each there
are.
A
I
B
J
D
H
G
Course 2
C
Type
Isosceles
F
How many
5
E
Name
DJA,
JDG
HJI,
BCD
DFE
Obtuse
2
DJA,
ADG
Acute
4
JDG,
JHI,
BCD,
DEF
8-6 Classifying
Insert Lesson
Triangles
Title Here
Lesson Quiz
Classify each triangle according to its sides and
angles.
1. 7ft, 8ft, 12ft scalene
2. 45°, 90°, 45° right
3. 12, 9, 12 isosceles
4. 120°, 20°, 40° obtuse
5. Identify the different types of triangles in the
figure and determine how many of each there are.
1 isosceles acute triangle, 1 equilateral
triangle, 1 scalene right triangle
Course 2