Download Obtuse Triangle

Warm Up
Classify each angle as acute, obtuse, or right.
1.
2.
acute
right
3.
obtuse
4. If the perimeter is 47, find x and the lengths of the
three sides.
x = 5; 8; 16; 23
Section 4-1:
Classifying Triangles
What we’re going to learn…
• How do classify triangles based
on the measures of their angles
and the length of their sides.
• How to use triangle
classifications to find measures
of angles and lengths of sides.
Aligning SC Standards
• G-1.8: Connect geometry with other
branch of mathematics
• G-3.1: Carry out a procedure to
compute the perimeter of a triangle.
• G-3.4: Apply properties of isosceles
and equilateral triangles to solve
problems.
What do you know? (Activate Prior Knowledge)
• What do you KNOW
• about triangles?
• What do you THINK you
know about triangles?
What you WILL know? (Lesson Preview)
• *
acute triangle
equiangular triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle
2 Ways to Classify Triangles
• By Angles
• By Sides
AB, BC, and AC are the sides of
ABC.
C
A
B
A, B, C are the triangle's vertices.
Triangle Classification By Angle Measures
Equiangular Triangle
Three congruent acute angles
Classifying Triangles by Angles
Equiangular
All the angles
are congruent
Triangle Classification By Angle Measures
Acute Triangle
Three acute angles
Classifying Triangles by Angles
Acute
All the angles
are acute
Triangle Classification By Angle Measures
Right Triangle
One right angle
Classifying Triangles by Angles
• Right
• One angle is
right or 90°
Triangle Classification By Angle Measures
Obtuse Triangle
One obtuse angle
Classifying Triangles by Angles
Obtuse
One angle is
obtuse
Examples – Classifying
Triangles by
Angles
• Classify the
triangle to the
left.
33°
57°
Examples – Classifying
Triangles by
Angles
• Classify the
triangle to the
left.
60 °
60°
60°
Examples – Classifying
Triangles by
Angles
• Classify the
triangle to the
left.
Examples – Classifying
Triangles by
Angles
• Classify the
triangle to the
left.
83.1°
44.7°
52.2°
You Try – Classifying
• Classify the
triangle to the
left.
60 °
60°
Triangles by Angles
60°
You Try – Classifying
Triangles by Angles
• Classify the
triangle to the
left.
45°
45°
You Try – Classifying
• Classify the
triangle to the
left.
88°
45°
Triangles by Angles
47°
You Try – Classifying
Triangles by Angles
• Classify the
triangle to the
left.
Example 1A: Classifying Triangles by Angle Measures
Classify
BDC by its angle measures.
B is an obtuse angle.
B is an obtuse angle. So
BDC is an obtuse triangle.
Example 1B: Classifying Triangles by Angle Measures
Classify
ABD by its angle measures.
ABD and CBD form a linear pair, so they are supplementary.
Therefore mABD + mCBD = 180°. By substitution,
mABD + 100° = 180°. So mABD = 80°. ABD is an acute triangle by
definition.
Check It Out! Example 1
Classify
FHG by its angle measures.
EHG is a right angle. Therefore mEHF +mFHG = 90°. By substitution, 30°+
mFHG = 90°. So mFHG = 60°.
FHG is an equiangular triangle by definition.
Triangle Classification By Side Lengths
Equilateral Triangle
Three congruent sides
Classifying Triangles by Sides
• Equilateral
• All sides are
congruent
Triangle Classification By Side Lengths
Isosceles Triangle
At least two congruent sides
Classifying Triangles by Sides
• Isosceles
• 2 sides are
congruent
Triangle Classification By Side Lengths
Scalene Triangle
No congruent sides
Classifying Triangles by Sides
• Scalene
• NO sides are
congruent
Remember!
When you look at a figure, you cannot
assume segments are congruent based
on appearance. They must be marked as
congruent.
Examples - Classifying Triangles by
Sides
• Classify the triangle to
the right.
Examples - Classifying Triangles by
Sides
• Classify the triangle to
the right.
Examples - Classifying Triangles by
Sides
• Classify the
triangle to the right.
You Try - Classifying Triangles by Sides
• Classify the triangle to
the right.
You Try - Classifying Triangles by Sides
• Classify the
triangle to the right.
You Try - Classifying Triangles by Sides
• Classify the triangle to
the right.
Example 2A: Classifying Triangles by Side Lengths
Classify
EHF by its side lengths.
From the figure,
isosceles.
. So HF = 10, and
EHF is
Example 2B: Classifying Triangles by Side Lengths
Classify
EHG by its side lengths.
By the Segment Addition Postulate, EG = EF + FG = 10 +
4 = 14. Since no sides are congruent, EHG is scalene.
Check It Out! Example 2
Classify
ACD by its side lengths.
From the figure,
isosceles.
So AC = 15, and
ACD is
Examples- Classifying Triangles Both Ways
• Classify the triangle to
the right.
117°
30°
33°
Examples- Classifying Triangles Both Ways
• Classify the triangle to
the right.
83°
48.5°
48.5°
Examples- Classifying Triangles Both Ways
• Classify the triangle to
the right.
60°
60°
60°
You Try - Classifying Triangles Both Ways
• Classify the triangle to
the right.
57°
33°
90°
You Try - Classifying Triangles Both Ways
• Classify the triangle to
the right.
45°
45°
You Try- Classifying Triangles Both Ways
• Classify the triangle to
the right.
61°
78°
41°
Example 3: Using Triangle Classification
Find the side lengths of
JKL.
Step 1 Find the value of x.
Given.
JK = KL
4x – 10.7 = 2x + 6.3
2x = 17.0
x = 8.5
Def. of  segs.
Substitute (4x – 10.7) for JK and (2x +
6.3) for KL.
Add 10.7 and subtract 2x from both
sides.
Divide both sides by 2.
Example 3 Continued
Find the side lengths of
JKL.
Step 2 Substitute 8.5 into the expressions
to find the side lengths.
JK = 4x – 10.7
= 4(8.5) – 10.7 = 23.3
KL = 2x + 6.3
= 2(8.5) + 6.3 = 23.3
JL = 5x + 2
= 5(8.5) + 2 = 44.5
Check It Out! Example 3
Find the side lengths of equilateral
FGH.
Step 1 Find the value of y.
Given.
FG = GH = FH
Def. of  segs.
3y – 4 = 2y + 3
Substitute
(3y – 4) for FG and (2y + 3) for
GH.
y=7
Add 4 and subtract 2y from
both sides.
Check It Out! Example 3 Continued
Find the side lengths of equilateral
FGH.
Step 2 Substitute 7 into the expressions to find the side lengths.
FG = 3y – 4
= 3(7) – 4 = 17
GH = 2y + 3
= 2(7) + 3 = 17
FH = 5y – 18
= 5(7) – 18 = 17
Example 4: Application
A steel mill produces roof supports by welding pieces
of steel beams into equilateral triangles. Each side of
the triangle is 18 feet long. How many triangles can be
formed from 420 feet of steel beam?
The amount of steel needed to make one triangle is
equal to the perimeter P of the equilateral triangle.
P = 3(18)
P = 54 ft
Example 4: Application Continued
A steel mill produces roof supports by welding pieces
of steel beams into equilateral triangles. Each side of
the triangle is 18 feet long. How many triangles can be
formed from 420 feet of steel beam?
To find the number of triangles that can be made
from 420 feet of steel beam, divide 420 by the amount
of steel needed for one triangle.
420  54 = 7
7
9
triangles
There is not enough steel to complete an eighth
triangle. So the steel mill can make 7 triangles from a
420 ft. piece of steel beam.
Check It Out! Example 4a
Each measure is the side length of an equilateral
triangle. Determine how many 7 in. triangles can be
formed from a 100 in. piece of steel.
The amount of steel needed to make one triangle is
equal to the perimeter P of the equilateral triangle.
P = 3(7)
P = 21 in.
Check It Out! Example 4a Continued
Each measure is the side length of an equilateral triangle. Determine how
many 7 in. triangles can be formed from a 100 in. piece of steel.
To find the number of triangles that can be made from 100 inches of
steel, divide 100 by the amount of steel needed for one triangle.
2
7
100  7 = 14 triangles
There is not enough steel to complete a fifteenth triangle. So the
manufacturer can make 14 triangles from a 100 in. piece of steel.
Check It Out! Example 4b
Each measure is the side length of an equilateral triangle.
Determine how many 10 in. triangles can be formed from
a 100 in. piece of steel.
The amount of steel needed to make one triangle is
equal to the perimeter P of the equilateral triangle.
P = 3(10)
P = 30 in.
Check It Out! Example 4b Continued
Each measure is the side length of an equilateral triangle. Determine how
many 10 in. triangles can be formed from a 100 in. piece of steel.
To find the number of triangles that can be made from 100 inches of
steel, divide 100 by the amount of steel needed for one triangle.
100  10 = 10 triangles
The manufacturer can make 10 triangles from a 100 in. piece of steel.
Homework (Choose 1 of the 3 options)
1. Make a set of flash cards. One card for each of
the 7 triangles. Put an image and name of each
triangle on one side and a description on the back.
2. List 7 real-world examples of where the 7 types of
triangles can be seen. For example: Doritos® as
equilateral triangles. (You cannot use mine )
3. Create a checklist of steps or things to check for
when classifying triangles. For example: Step 1 –
Examine the angle measures, etc.
Exit Slip
• In your brain, answer the following
questions:
• What did you learn today? Which of the 7
triangles is your favorite and why?