Download Lesson 4.1

Lesson 4.1
Section 4.1: Apply Triangle Sum Properties ~ 10.8.09
In Your Notes, draw the pictures and classify the following triangles (by sides):
~ Isosceles ~ Equilateral ~ Scalene ~
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Lesson 4.1
In Your Notes, draw the pictures and classify the following triangles (by sides):
~ Isosceles ~ Equilateral ~ Scalene ~
scalene triangle ‐ No Congruent Sides
isosceles triangle ‐ At least 2 Congruent Sides
equilateral triangle ‐ All 3 sides are Congruent
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Lesson 4.1
In Your Notes, draw the pictures and classify the following triangles (by angles):
~ Right triangle ~ Acute Triangle ~
~Equiangular Triangle ~ Obtuse Triangle ~
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Lesson 4.1
In Your Notes, draw the pictures and classify the following triangles (by angles):
~ Right triangle ~ Acute Triangle ~
~Equiangular Triangle ~ Obtuse Triangle ~
Acute Triangle
(3 Acute Angles)
Obtuse Triangle
(1 Obtuse Angle)
Equiangular Triangle
(3 Congruent Angles)
Right Triangle
(1 Right Angle)
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Lesson 4.1
Interior angles vs Exterior angles
which angles are which?
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Interior angles: the original angles
formed inside the three sides
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Exterior angles: angles that form
linear pairs with the interior angles
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Lesson 4.1
Exterior angles: angles that form
linear pairs with the interior angles
What about these?
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Lesson 4.1
The Triangle Sum Theorem
(Theorem 4.1): The sum of the interior
B
angles of any triangle is 180o
C
A
m
A+m
B+m
C = 180o
OR
orange angle + green angle + purple angle = 180o
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Lesson 4.1
Exterior Angle Theorem
(Theorem 4.2): The measure of an exterior angle
of a triangle is equal to the sum of the measures
of the two nonadjacent interior angles
B
C
1
A
REMINDER
exterior angle: make a linear pair with the interior angles
.
adjacent: next to. ‐‐> So nonadjacent: NOT next to
.
interior angle: angles formed inside the three sides
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Lesson 4.1
Theorem 4.2: The measure of an exterior angle of
a triangle is equal to the sum of the measures of
the two nonadjacent interior angles
B
C
1
m
B+m
A
C=m
1
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Lesson 4.1
A corollary (to a theorem) is a statement that
can be proved easily using the theorem.
Corollary(to the Triangle Sum Theorem ‐ 4.1):
The acute angles of a right triangle are complementary
C
A
B
m A + m B = 90o
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Lesson 4.1
TRIANGLE
ACTIVITY!!
yes, this took a long time and yes it was unnecessary
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B
A
C
because we love activities
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B
A
C
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B
B
A
A
C
C
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B
B
C
A
A
C
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B
B
C
A
C
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B
Example 3, pg. 87 (guides)
(3x ­ 9)
o
73o
D
C
xo
A
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J
Example 3, pg. 219 (books)
xo
70o
L
(2x ­ 5)o
K
M
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Lesson 4.1
Miss Willson's
Homework Policy
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Lesson 4.1
Homework
pg 221 (1‐7, *14‐19, 21‐26, 31‐34)
*If you can show me that you can do 15, 16, and 18 correctly, then you don't need to do the other three problems!
.
~You must show ALL of your work in all three problems in order for 14, 17 and 19 to be excused. ~it's okay if they are out of order on your homework
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