Download Triangle Angle Sum

October 24, 2016
Unit 3, Lesson 5
Triangle Angle Sum
I am interested in mathematics only as a creative art.
- G. H. Hardy
Triangle
-the figure formed by segments joining three noncollinear points.
Parts of a Triangles
Vertex - one of the three points (plural - vertices)
Sides - the segments
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Triangle ABC ( ΔABC)
Vertices - A, B, C
Sides - AB, BC, CA
Classifications by Sides
Scalene Triangle
- no congruent sides
Isosceles Triangle
- at least two congruent sides
Equilateral Triangle
- Three congruent sides
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Classification by Angles
Acute Triangle
- three acute angles
Right Triangle
- one right triangle
Obtuse Triangle
- one obtuse angle
Equiangular Triangle
- all three angles are congruent
When classifying angles you may use a side
and an angle classification together.
Example: Acute scalene triangle, Isosceles right triangle,
scalene obtuse triangle.
Note:
Not all combinations are possible to create.
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Cut out triangle ABC
Cut off angles A, B and C.
Place angles below to form a straight angle.
What does this imply about the angles of a triangle?
Theorem 3-11 - Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180
Given: ΔABC
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Corollary
- a statement which can be proved easily by applying a theorem
- Corollaries can be used as reasons in proofs
Corollary 1 to Theorem 3-11 (Third Angle Theorem
If two angles of one triangles are congruent to two angles
of another triangle, then the third angles are congruent.
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Corollary 2 to Theorem 3-11
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Each angle of an equiangular triangle measures 60
Corollary 3 to Theorem 3-11
In a triangle, there can be at most one right angle
or one obtuse angle.
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Corollary 4 to Theorem 3-11
The acute angles of a right triangle are complementary
Example 1: Find the value of x and y
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Example 2: Find the value of x
Example 3: The angles of a triangle are in the ratio 1:2:3.
What are the measures of the angles?
October 24, 2016
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What did we rely on to prove a triangle has 180 ?
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Could we show the sum is 180 without this assumption?