Section 33, Parallel Lines and the Triangle AngleSum Theorem

1

• 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 m?1.
• m?1 35 65 180
• m?1 100 180
• m?1 80

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
• and angles.

Acute Isosceles
6

• 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
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

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