Title: Section 33, Parallel Lines and the Triangle AngleSum Theorem
Section 3-3 Parallel Lines and the Triangle Angle-Sum Theorem
Draw and cut out a large triangle.
Number the angles and tear then off.
Place the three angles adjacent to each other form one straight angle.
a. What can you say about the sum of the measures of the angles of a triangle
2 3 1 2
Theorem 3-7 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180o.
Example Find m1.
m1 35 65 180
m1 100 180
C B A 1 65o 35o 3
Student example Find the values of x y and z.
G 39 65 X 180 104 X 180 X 76 39o 21o X Y 180 76 Y 180 Y 104 65o zo yo xo F H J 21 104 Z 180 125 Z 180 Z 55 How could we use GFH instead of GJH to find the value of z. For GFH 65 (39 21) Z 180 Then 125 Z 180 and Z 55 4
Student example In triangle ABC ACB is a right angle and CD AB. Find the values of a b and c.
C 70o co ao bo B A D c 20 b 20 a 70 5
Classifying a triangle by its angles and sides.
Equiangular all angles congruent
Acute all angles acute
Right one right angle
Obtuse one obtuse angle
Equilateral all sides congruent
Isosceles at least two sides congruent
Scalene no sides congruent
Classify the triangle by its sides
Acute Isosceles 6
Draw and mark a triangle to fit each description. If no triangle can be drawn write not possible and explain why.
Not possible an equilateral triangle has all acute angles 7
Exterior angle of a polygon is an angle formed by a side and an extension of an adjacent side. For exterior angles of a triangle the two nonadjacent interior angles are its remote interior angles.
Exterior angle 1 3 2 Remote interior angles 8
Theorem 3-8 Triangle Exterior Angle Theorem The measures of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
2 1 3 9
Example find the measure of the missing angle.
2 113o 70o 10
Student example find the measure of the missing angle.
40o 1 30o 11
Student example Explain what is wrong with this diagram.
The measure of the exterior angle needs to be greater than either remote interior angles.
B 80o 85o C A D 12
Questions 2-8 14-18 26 27 31 32 38
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