Download 1- Classifying Triangles

Triangles and Angles
“I can classify triangles by sides and angles.”
“I can find angle measures inside triangles.”
By PresenterMedia.com
Names of Triangles
By sides
Equilateral
All sides 
Isosceles
2 sides 
Scalene
No sides 
Names of Triangles
By angles
Acute
3 acute angles
Equiangular
3 congruent
angles
Right
1 right angle
Obtuse
1 obtuse angle
Mix and Match
Use two names to describe this:
Mix and Match
Use two names to describe this:
Mix and Match
Use two names to describe this:
It can be proven:
Equilateral triangles are always equiangular;
And equiangular triangles are always equilateral.
In general, a triangle is named by its vertices.
This one is called ∆𝐴𝐵𝐶:
A
C
B
Always label clockwise; always go in alphabetical order.
Anatomy
What are the parts called?
A corner is called a
vertex.
Two or more corners
are called vertices.
Anatomy
What are the parts called?
Two sides sharing
a common vertex
are adjacent.
“next to”
Anatomy: Legs
Right triangles and isosceles triangles have legs.
hypotenuse
leg
leg
leg
leg
base
Construction workers lay out a right angle
Its called the 3-4-5 method.
Interior or Exterior Angles
Interior
Exterior
Triangle Sum Theorem
TST
If you add together all the angles of a triangle,
the sum will always be 180 degrees.
In other words…
If you know 2 angles of a triangle,
you can always find the third.
“Proof”
Convincing argument why it must be true.
Teacher Example #1
Watch and take notes
52
27
x
Teacher Example #2
Watch and take notes
36
(7x + 1)
(x -9)
Student Practice
Do these problems. Solve for x. Find all angles. Classify by name.
1.
2.
x
24
x
3.
72
17
(x + 24)
(x - 15)
(x + 54)
131
4.
x
7x
2x
1.
Solve for x. Find all angles. Classify by name.
24
x
72
2.
Solve for x. Find all angles. Classify by name.
x
131
17
3.
Solve for x. Find all angles. Classify by name.
(x + 24)
(x - 15)
(x + 54)
4.
Solve for x. Find all angles. Classify by name.
x
7x
2x
Corollary to the Triangle Sum Theorem
Corollary = a statement easily proven
In a right triangle, the two acute angles
add up to 90.
Exterior Angle Theorem
EAT
An exterior angle is equal to the sum of the two
interior angles not adjacent to it.
Teacher Example #3
Watch and take notes
52
27
x
Teacher Example #4
Watch and take notes
38
(7x + 1)
(10x + 9)
Student Practice
Do these problems. Solve for x. Find all angles.
5.
6.
25
49
71
x
(4x + 1)
(8x + 10)
5.
49
71
x
6.
25
(4x + 1)
(8x + 10)
“I can classify triangles by sides and angles.”
• “I can find angle measures inside triangles.”
•
Solve for x. Then find the measure of all angles.
Finally, classify the triangle using two names.
36°
x°
72°
y°
Solve
Then find
measure of
all angles.
Solve for
for x.
x. Then
find the
the measure
of all
angles.
Finally,
classify the
the triangle
using two
two names.
names.
Finally, classify
triangle using
36°
36°
72°
x°
y°
x°
72°
y°