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8-2. Classifying Angles. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 8-2. Classifying Angles. Course 2. Warm Up. 1. What percent of the model is shaded?. 71%. 2. Find the value of 5 2 + 5 3. 150. What is the percent of change if 20 is increased to 25?. 25%. - PowerPoint PPT Presentation
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8-2 Classifying Angles
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm Up
Course 2
8-2 Classifying Angles
1. What percent of the model is shaded?
2. Find the value of 52 + 53.
3. What is the percent of change if 20 is increased to 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?
71%
150
25%
1.08 m
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.
Angles are measured in degrees (°).
A
CB
1
Vertex
Course 2
8-2 Classifying Angles
Learn to identify angles and angle pairs.
An angle’s measure determines the type of angle it is.
A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.
An obtuse angle is an anglethat measures more than 90°but less than180°.
A straight angle is an anglethat measures 180°.
Course 2
8-2 Classifying Angles
Tell whether each angle is acute, right, obtuse or straight.
A. B.
obtuse angle acute angle
Course 2
8-2 Classifying Angles
Insert Lesson Title Here
Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
Course 2
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
Course 2
8-2 Classifying Angles
COmplementary
upplementary
C C= 90˚
= 180˚
+ 90˚
C
Course 2
8-2 Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B • • C
1
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-2 Classifying Angles
Since 60° + 30° = 90°, PMQ and OMP are complementary.
O
P Q
M
OMP and PMQ
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-2 Classifying Angles
O
N R
M
Since 15° + 165° = 180°, NMO and OMR are supplementary.
Read mNMO as “the measure of angle NMO.”
Reading Math
NMO and OMR
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Course 2
8-2 Classifying Angles
PMQ and QMR P Q
RM
Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.
Angles A and B are complementary.
If mA is 56°, what is the mB?
Course 2
8-2 Classifying Angles
Angles P and Q are supplementary.
If mP is 32°, what is the mQ?
One way to classify triangles is by the lengths of their sides.
Course 2
8-6 Classifying Triangles
Learn to classify triangles by their side lengths and angle measures.
Triangles classified by sides
A scalene trianglehas no congruent sides.
Course 2
8-6 Classifying Triangles
Triangles classified by sides
An isosceles trianglehas 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 hasone 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. Two congruent sidesacute Three acute angles
This is an isosceles acute triangle.
B. No congruent sidesright One right angle
This is a scalene right triangle.
isosceles
scalene
Course 2
8-6 Classifying Triangles
Classify each triangle according to its sides and angles.
C. Three congruent sides
acute Three acute angles
This is an equilateral acute triangle.
equilateral
Course 2
8-6 Classifying Triangles
D. No congruent sides
obtuse One obtuse angle (exceeds 90°)
This is a scalene obtuse triangle.
scalene
Insert Lesson Title Here
Classify each triangle according to its sides and angles.
E. Two congruent sidesobtuse One obtuse angle
This is an isosceles obtuse triangle.
F. Two congruent sides
right One right angle
This is an isosceles right triangle.
isosceles
isosceles
Course 2
8-6 Classifying Triangles
Identify the different types of triangles in the figure, and determine how many of each there are.
Type How many Name
Scalene 2 ABD, BCD
Isosceles
Right
Obtuse
Acute
ACE, ABC
ABD, BCD
ACE
ABC
2
2
1
1
Course 2
8-6 Classifying Triangles
Insert Lesson Title Here
A
BC
D
EF
G
H
I J
Identify the different types of triangles in the figure, and determine how many of each there are.
Isosceles
Obtuse
Acute
5
2
4
NameHow manyType
DJA, JDG
HJI, BCD
DFE
DJA, ADG
JDG, JHI,
BCD, DEF
Course 2
8-6 Classifying Triangles
Lesson Quiz
Classify each triangle according to its sides and angles.
1. 7ft, 8ft, 12ft
2. 45°, 90°, 45°
3. 12, 9, 12
4. 120°, 20°, 40°
5. Identify the different types of triangles in the figure and determine how many of each there are.
right
scalene
Insert Lesson Title Here
isosceles
obtuse
1 isosceles acute triangle, 1 equilateral triangle, 1 scalene right triangle
Course 2
8-6 Classifying Triangles
