Download Notes Sec 4.1.notebook

Notes Sec 4.1.notebook
Unit 4: Classifying Triangles (4.1) p.194­201
Triangle: a figure formed by 3 segments that join 3 noncollinear points
A triangle can be named using its sides or its angles
Recall some definitions:
Vertex: points where the angles are formed in the triangle
Adjacent sides: 2 sides sharing a common vertex
opposite
side of
< A
C
adjacent sides
A
B
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Notes Sec 4.1.notebook
Hypotenuse:the opposite side of the right angle
Legs:the sides that form the right angle of a right triangle
­­the congruent sides of an isosceles triangle­­
leg
hypotenuse
leg
leg
leg
base
Exterior Angles
In an isosceles triangle, we
refer to the base and the legs.
base angles are also congruent
Interior Anlges
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Names of Triangles
Classified by Sides:
Equilateral: 3 sides congruent
Equilateral triangles
also equiangular
(equal angles)!
Isosceles:
At least 2 sides congruent
Scalene:
No Sides Congruent
Base angles of an isosceles
triangle are congruent!
Classified by Angles:
Acute:
3 acute angles
Equiangular:
3 congruent angles
(also acute and 3 sides
are congruent)
Right:
1 right angle
Obtuse:
1 obtuse angle
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Notes Sec 4.1.notebook
Warm­up Problems:
True or False (#1­4)
1. It is possible to draw an acute scalene triangle.
2. It is possible to draw an obtuse equilateral triangle. 3. It is possible to draw a right isosceles triangle.
4. It is possible to draw a right scalene triangle.
5. Classify the triangle with the most specific name possible:
46O
46O
88O
Sec. 4.1 (continued)
Triangle Sum Theorem: ­ the sum of the measures of the interior
angles of a triangle is 180 degrees.
m<A + m<B + m<C = 180 o
B
A
C
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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.
m<1 = m<A + m< B
A
1
B
Exterior Angles Facts:
0
1. the sum of the exterior angles of a triangle is 360
2. an exterior angle is equal to the sum of its 2 remote interior angles (the non­adjacent angles)
Exterior Angles
Interior Anlges
An exterior angle forms a linear pair with its adjacent interior angle, so they sum to what?
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Corollary to the Triangle Sum Theorem:
The acute angles of a right triangle are complementary.
m<A + m<B = 90 o
A
B
Solve for x.
2.
1.
2x0
3x0
(4x + 8)0
(2x ­ 15)0
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3.
4. Classify the triangle
by sides and angles.
360
50
23
19
770
5.
110
x0
20
16
6. An equilateral triangle has 1 angle measure of 4x0. What is the value of x?
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7.
8.
(5x + 4)0
(4x ­8)0
420
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