Download 4.3 Angle Relationships in Triangles.notebook

4.3 Angle Relationships in Triangles.notebook
November 01, 2016
In your Foldable (Classifying Triangles)
Exterior ∠ Τheroem
m∠1 + m∠2 = m∠4
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4.3 Angle Relationships in Triangles.notebook
November 01, 2016
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4.3 Angle Relationships in Triangles.notebook
November 01, 2016
What we will learn today:
• Find the measures of interior &
exterior angles of triangles.
• Apply theorems about the
interior & exterior angles of
triangles.
Angle Sum Theorem
The sum of the measures of the angles of a
triangle is 180°
Auxiliary Line
> intersects one angle of the triangle
> parallel to the opposite side
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4.3 Angle Relationships in Triangles.notebook
November 01, 2016
A corollary is a theorem whose proof follows directly
from another theorem.
Here is a corollary to the Triangle Sum Theorem:
In your foldable (Special Triangles and Formulas)
The acute angles of a right triangle are complementary.
Examples ~
(a) Find the missing angle measures in the triangles
below.
Examples ~
(a) One of the acute angles in a right triangle measures
63.7°. What is the measure of the other acute
angle?
(b) The measure of one of the acute angles in a right
triangle is 2x°. What is the measure of the other
acute angle?
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4.3 Angle Relationships in Triangles.notebook
November 01, 2016
An interior angle is formed by two sides of a triangle.
An exterior angle is formed by one side of the triangle
and extension of an adjacent side.
A remote interior angle is an interior angle that is not
adjacent to the exterior angle.
In your Foldable (Classifying Triangles)
Exterior ∠ Τheroem
m∠1 + m∠2 = m∠4
Examples ~
(a) Find m∠B in
ABC.
(b) Find m∠Α in
ABC.
(c) Find all the missing ∠ measures in the figure.
72°
100°
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4.3 Angle Relationships in Triangles.notebook
November 01, 2016
Examples ~
(a) Find m∠K and m∠J.
(b) Find m∠P and m∠T.
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