Download Angles and triangles.notebook

Angles and triangles.notebook
October 03, 2016
Section 3­4 Angles of Triangles
What is a triangle?
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Angles and triangles.notebook
October 03, 2016
Triangles
• Definition
• A figure where three segments join at three points • Vertex
• Sides 2
Angles and triangles.notebook
October 03, 2016
Classifying or Describing Triangles
• Sometimes by the number of congruent SIDES
• Sometimes by the its ANGLES
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Angles and triangles.notebook
October 03, 2016
Classifying by Sides
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Scalene triangle
No congruent sides
Isosceles triangle
At least two congruent sides
Equilateral triangle
All sides congruent 4
Angles and triangles.notebook
October 03, 2016
Classifying by Angles
• Acute
• Obtuse
• Right
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Three acute angles
One obtuse angle
One right angle
All congruent angles
• Equiangular
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Angles and triangles.notebook
October 03, 2016
Side Note
• Often diagrams needed for proofs are lacking elements.
• If this is the case an AUXILIARY LINE (or ray or segment) can be drawn to help with the proof.
• AUXILIARY LINES are denoted using a dotted/dashed line.
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Angles and triangles.notebook
October 03, 2016
Theorem 3­11 The sum of the measures of the angles of a triangle is 180.
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Angles and triangles.notebook
October 03, 2016
Practice
Find the missing angle then state whether the triangles are acute, obtuse or right
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1. 55, 43
2. 47,43
3. 80,75
4. 33, 33
5. 24, 66
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Angles and triangles.notebook
October 03, 2016
Now that we have theorem 3­11 What can be said about equiangular triangles?
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Angles and triangles.notebook
October 03, 2016
Corollary 2
Each angle of an equiangular triangle is 60°.
Draw me a equiangular triangle.
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Angles and triangles.notebook
October 03, 2016
Using theorem 3­11 Can a triangle have two angles greater than or equal to 90°?
Draw me a triangle with two obtuse angles? Can it be done? What about with two right anlges?
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Angles and triangles.notebook
October 03, 2016
Corollary 3
In a triangle, there can be at most one right or obtuse angle.
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Angles and triangles.notebook
October 03, 2016
Using theorem 3­11
In a right triangle what can be said about the two other angles?
Draw me a right triangle and make a conclusion about the other two angles.
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Angles and triangles.notebook
October 03, 2016
Corollary 4
The acute angles of a right triangle are complementary.
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Angles and triangles.notebook
October 03, 2016
Corollary 1
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
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Angles and triangles.notebook
October 03, 2016
Theorem 3­12
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
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Angles and triangles.notebook
October 03, 2016
CE on p.96
Homework:Written exercises pg 97 #1­18
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