Download 3.6 - Classifying Triangles (and 3.7).notebook

3.6 ­ Classifying Triangles (and 3.7).notebook
October 30, 2015
Bellringer: Find the value of x below
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3.6 ­ Classifying Triangles
Classifying Triangles by Angle Measures
Classifying Triangles by Side Lengths
• Scalene Triangle = No congruent sides
• Isosceles Triangle = At least 2 congruent sides
• Equilateral Triangle = All 3 sides congruent
• Acute Triangle = 3 acute angles
• Right Triangle = 1 right angle, 2 acute
• Obtuse Triangle = 1 obtuse angle, 2 acute
• Equiangular Triangle = All 3 angles congruent
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Type of Triangles in proofs
Proof Example #1
Def: Isosceles Triangle ­­> 2 sides congruent
A
Vertex Angle
Given:
C
E
Statements
Leg
Leg
C
B
Reasons
is isosceles 1.) Given
3.)
2.) If a triangle is isosceles, then it has at least 2 congruent sides.
3.) Given
4.)
4.) Reflexive Property
5.)
5.) SSS (2,3,4)
2.)
D
is isosceles with base CD Prove: 1.)
O
Base
Base Angles
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3.6 ­ Classifying Triangles (and 3.7).notebook
3.6 Homework ­ Problem #5
C
Given:
Statements
Reasons
1.)
1.) Given
2.)
2.) Thm: All radii 3.)
is isosceles
Things You Can Assume from Diagram
1.
Straight Angles/Lines
2.
Supplementary Angles
3.
Vertical Angles
4.
Reflexive Property
O
is isosceles
Prove: D
October 30, 2015
3.) Def: Isosceles Triangle
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3.6 Homework ­ Problem #11
V
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3.7 (Cont.)
A
Thm: If two sides in a triangle are congruent, then the angles opposite those sides are also congruent.
If sides, then angles
If , then Y
S
Thm: If two angles in a triangle are congruent, then the sides opposite B
those angles are also congruent.
C
If angles, then sides
­
• Triangle VSY Isosceles
• Perimeter < 45
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If , then Sep 29­9:06 AM
3.7 (Cont.)
Thm: If two sides of a triangle are not congruent, then the angles opposite the sides are not congruent. Also:
Larger angle <­­> Larger side
and
Smaller angle <­­> Smaller side
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