Angles of Triangles

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Angles of Triangles

• 3-4

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EXAMPLE 1
Classify triangles by sides and by angles
SOLUTION
The triangle has a pair of congruent sides, so it
is isosceles. By measuring, the angles are 55 ,
55 , and 70 . It is an acute isosceles
triangle.
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EXAMPLE 2
Classify a triangle in a coordinate plane
SOLUTION
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EXAMPLE 2
Classify a triangle in a coordinate plane
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for Examples 1 and 2
GUIDED PRACTICE
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for Examples 1 and 2
GUIDED PRACTICE
SOLUTION
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for Examples 1 and 2
GUIDED PRACTICE
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EXAMPLE 3
Find an angle measure
SOLUTION
Apply the Exterior Angle Theorem.
Solve for x.
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EXAMPLE 4
Find angle measures from a verbal description
SOLUTION
First, sketch a diagram of the situation. Let the
measure of the smaller acute angle be x . Then
the measure of the larger acute angle is 2x .
The Corollary to the Triangle Sum Theorem states
that the acute angles of a right triangle are
complementary.
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EXAMPLE 4
Find angle measures from a verbal description
Use the corollary to set up and solve an equation.
Corollary to the Triangle Sum Theorem
Solve for x.
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for Examples 3 and 4
GUIDED PRACTICE
SOLUTION
Apply the Exterior Angle Theorem.
Solve for x.
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for Examples 3 and 4
GUIDED PRACTICE
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for Examples 3 and 4
GUIDED PRACTICE
SOLUTION
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for Examples 3 and 4
GUIDED PRACTICE
SOLUTION
Use the corollary to set up solve an equation.
Corollary to the Triangle Sum Theorem
Solve for x.
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for Examples 3 and 4
GUIDED PRACTICE
SOLUTION
First, sketch a diagram of the situation. Let the
measure of the smaller acute angle be x . Then
the measure of the larger acute angle is 2x .
The Corollary to the Triangle Sum Theorem states
that the acute angles of a right triangle are
complementary.
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for Examples 3 and 4
GUIDED PRACTICE
Use the corollary to set up and solve an
equation.
Corollary to the Triangle Sum Theorem
Solve for x.