Download 4.1 triangle sum.notebook

4.1 triangle sum.notebook
October 16, 2014
10/16/14 - Warm Up Problem
Graph each line.
1. y = -2x + 5
2. 2x - 3y = 9
Oct 15­3:49 PM
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4.1 triangle sum.notebook
October 16, 2014
Section 4.1 - Apply Triangle Sum Properties
Goal: classify triangles calculate angle measures of triangles
Classifying Triangles by Angle Measure
Acute Triangle: all three angles are acute
Obtuse Triangle: one angle is obtuse
acute
obtuse
Right Triangle: one angle is right
right
Equiangular Triangle: an acute triangle with all three angles congruent
Oct 14­10:25 AM
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4.1 triangle sum.notebook
October 16, 2014
Classifying Triangles by Side Length
Equilateral: all three sides of the triangle are congruent
7
7
7
Isosceles: at least two sides of the triangle are congruent
7
7
11
Scalene: no sides of the triangle are congruent
8
7
10
Oct 14­10:27 AM
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4.1 triangle sum.notebook
October 16, 2014
Theorem 4.1 - Triangle Sum Theorem
The sum of the measures of the interior
angles of a triangle is 180o.
B
C
A
Oct 9­4:20 PM
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4.1 triangle sum.notebook
October 16, 2014
Proving the Triangle Sum Theorem
Given: ΔABC, PC || AB
Prove: m<A + m<B + m<2 = 180
P
C
1 2 3
A
Statements
Reasons
1. PC || AB
1. Given
2. <A≅<1
2. Alt. Int. Angles Thm.
3. <B≅<3
3. Alt. Int. Angles Thm.
4. m<1 + m<2 + m<3 = 180
4. Angle Addition Post.
5. m<A + m<2 + m<B = 180
5. Substitution Prop.
B
Oct 14­10:10 AM
5
4.1 triangle sum.notebook
October 16, 2014
Find the measure of each numbered angle.
3
1
28o
2
55o
Oct 9­4:30 PM
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4.1 triangle sum.notebook
October 16, 2014
Exterior Angles of Triangles
Exterior Angle: formed by one side of a triangle and the extension of another side
Theorem 4.2 - Exterior Angle Theorem
The measure of an exterior angle of a
triangle is equal to the sum of the measures
of the two nonadjacent interior angles.
B
1
C
A
Oct 14­10:30 AM
7
4.1 triangle sum.notebook
October 16, 2014
Find the measure of each numbered angle.
35o
75o
65o
100 o
Oct 14­10:34 AM
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4.1 triangle sum.notebook
October 16, 2014
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are
complementary.
A
B
C
Oct 15­4:20 PM
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4.1 triangle sum.notebook
October 16, 2014
Assignment:
pg. 221
(1-6)
(14-16)
(21-26)
Oct 9­4:56 PM
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