Download Lesson

Lesson 4-1
Classifying Triangles
Transparency 4-1
5-Minute Check on Chapter 3
Refer to the figure.
1. What is the special name given to the pair of angles
shown by 2 and 6?
2. Find m3.
3. Find m4.
4. Find the slope of the line that contains the points at (4, 4) and
(2, –5).
5. Write the equation of a line in slope-intercept form that has a slope of
¾ and contains the point at (0, 5).
6.
Standardized Test Practice:
What is the slope of a line that is perpendicular
to the line y = 2/3x – 5?
A
–3/2
B
–2/3
C
2/3
D
3/2
Transparency 4-1
5-Minute Check on Chapter 3
Refer to the figure.
1. What is the special name given to the pair of angles
shown by 2 and 6?
corresponding angles
2. Find m3.
62
3. Find m4.
118
4. Find the slope of the line that contains the points at (4, 4) and
(2, –5).
9/2
5. Write the equation of a line in slope-intercept form that has a slope of
¾ and contains the point at (0, 5).
y = 3/4x + 5
6.
Standardized Test Practice:
What is the slope of a line that is perpendicular
to the line y = 2/3x – 5?
A
–3/2
B
–2/3
C
2/3
D
3/2
Objectives
• Identify and classify triangles by angles
• Identify and classify triangles by sides
Vocabulary
• Scalene – no sides are congruent
• Isosceles – two sides are congruent
• Equilateral – all sides are congruent
• Equiangular – all angles are congruent
… By angles
Acute triangle
All angles < 90
Classifying Triangles
Obtuse triangle
One angle > 90
Right triangle
One angle = 90
… By sides
Scalene triangle
No sides are 
Isosceles triangle
Equilateral triangle
Two sides are 
All sides are 
Classify by
angle measure
Classifying Triangles
Classify by number
of congruent sides
Angles
Measure of
one angle
is 90°
Measure of
one angle
> 90°
Measure of
all angles
< 90°
3 congruent
angles
Sides
Right
Scalene
No sides
congruent
Isosceles
2 sides
congruent
Equilateral
3 sides
congruent
Obtuse
Acute
Equiangular
ARCHITECTURE The triangular truss below is modeled
for steel construction. Classify JMN, JKO, and OLN
as acute, equiangular, obtuse, or right.
Answer:
JMN has one angle with measure
greater than 90, so it is an obtuse
triangle.
JKO has one angle with
measure equal to 90, so it
is a right triangle.
OLN is an acute triangle with all angles congruent, so it
is an equiangular triangle.
ARCHITECTURE The frame of this window design is
made up of many triangles. Classify ABC, ACD, and
ADE as acute, equiangular, obtuse, or right.
Answer: ABC is acute.
ACD is obtuse.
ADE is right.
Identify the indicated triangles in the figure if
Isosceles triangles
Isosceles triangles have at least two
sides congruent.
Answer: UTX and UVX are
isosceles.
Scalene triangles
Scalene triangles have no congruent sides.
Answer: VYX, ZTX, VZU, YTU, VWX,
ZUX, and YXU are scalene.
Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, EBC, DEB, DCE, ADC, ABD
ALGEBRA Find d and the measure of each side of
equilateral triangle KLM if KL = d + 2, LM = 12 – d and
KM = 4d – 13.
Since KLM is equilateral, each side
has the same length. So KL = KM.
Substitution
Subtract d from each side.
Add 13 to each side.
Divide each side by 3.
Next, substitute to find the length of each side.
Answer: For KLM,
and the measure of
each side is 7.
ALGEBRA Find d and the measure of each side of
equilateral triangle
if
and
Answer:
COORDINATE GEOMETRY Find the measures of the
sides of RST. Classify the triangle by sides.
Use the distance formula to find the lengths of each side.
Answer:
; since all 3 sides
have different lengths, RST is scalene.
Find the measures of the sides of ABC. Classify the
triangle by sides.
Answer:
; since all 3 sides
have different lengths, ABC is scalene.
Summary & Homework
• Summary:
– Triangles can be classified by their angles as
acute, obtuse or right
– Triangles can be classified by their sides as
scalene, isosceles or equilateral
• Homework:
– pg 238-9: 4-6, 9-11, 15-20, 32-35