Download Parallel Lines and the Triangle Angle ‐ Sum Theorem

Geometry
3.4 ‐ Parallel Lines and the Triangle Angle ‐ Sum Theorem
A. Triangle Angle ‐ Sum Theorem: The sum of the measures of the angles of a triangle is 180⁰
B
m<A + m<B + m<C = 180
A
C
Oct 13­7:12 AM
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B. Examples. Find the missing angle measures.
1.
S
2.
A
1
1
C
770
R
1000
810
T
480
B
X 3.
4. 700
3
2
W
1
2
Y
350
Z
1
Oct 13­7:15 AM
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C. Classifying Triangles
(1)
Equilangular triangle ‐ a triangle with all angles congruent
(2)
Acute triangle ‐ a triangle with all angles acute
(3)
Right triangle ‐ a triangle that contains a right angle
(4)
Obtuse triangle ‐ a triangle that contains one obtuse angle
(5)
Equilateral triangle ‐ a triangle with all sides congruent
(6)
Isosceles triangle ‐ a triangle with at least two sides congruent
(7)
Scalene triangle ‐ a triangle that has no congruent sides
Draw an example of each type of triangle. Label the triangle as needed.
Oct 13­8:56 AM
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D. For 5, and 6 classify the following triangles. For 7 and 8, draw a triangle that fits such a description
6.
5. 8. Equilateral right
7. Scalene
Oct 13­8:57 AM
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E. Definitions and the Triangle Exterior Angle Theorem
• Exterior Angle of a Polygon ‐ an angle formed by a side and an extension of an adjacent side
• Remote Interior Angle ‐ two angles that are non‐adjacent to an exterior angle
3
2
6
5
1
4
• Triangle Exterior Angle Theorem ‐ the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
2
m<1 = m<2 + m<3
1
3
Oct 13­8:59 AM
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F. Examples. Use the Triangle Exterior Angle Theorem to find the measure of each numbered angle.
1.
2.
(x + 7)0
1
1
600
180
3. 1370
980
320
1
Oct 13­9:00 AM
6
3.4 HW p. 150 #s 1 ­ 6, 11 ­ 25 (17 just part b), 28, Oct 13­9:00 AM
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