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- 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

- Theorem 3-7, Triangle Angle-Sum Theorem The sum

of the measures of the angles of a triangle is

180o. - Example Find m?1.
- m?1 35 65 180
- m?1 100 180
- m?1 80

C

B

A

1

65o

35o

- 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

- 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

- 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
- and angles.

Acute Isosceles

- Draw and mark a triangle to fit each description.

If no triangle can be drawn, write not possible

and explain why. - Acute scalene
- Isosceles right
- Obtuse equiangular

Not possible an equilateral triangle has all

acute angles

- 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

- 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

- Example find the measure of the missing angle.

2

113o

70o

- Student example find the measure of the missing

angle.

40o

1

30o

- 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

- Homework
- Page 134-136
- Questions 2-8, 14-18, 26, 27, 31, 32, 38

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