Notes on 4-2

1. CLASSIFYING TRIANGLES and
THE TRIANGLE INTERIOR
ANGLE SUM THEOREM
Jim Smith
4-1 and 4-2 3108.4.9

2. Classifying by Angles
Acute Triangle
Has three acute angles
Obtuse Triangle
Has one obtuse angle
Right Triangle
Has one right angle

3. Classifying by sides
Equilateral Triangle
All three sides are congruent
Isosceles Triangle
Two of the sides are congruent
Scalene Triangle
No sides are congruent

4. • Classify the triangle by the
sides and angles.
8 in
8 in
Isosceles right triangle
Equilateral acute triangle

5. • Classify each triangle by its
sides and angles.
Isosceles obtuse triangle
Scalene obtuse triangle
Scalene right triangle

6. If you add up the measures of the
interior angles of a triangle, What is
the total?
180º
25º
65º

7. How many lines can be drawn
through point B that would become
parallel to M
m
B

8. Unique Parallel line Postulate –
Through a point not on a given line,
there is one and only one line parallel
to the given line.
m
B

9. Given:
Prove:
1. ABC is a triangle
2. Draw helping line
through B so that
3.
4.
5.
6.
7.
1. Given
2. Unique Parallel Postulate
3. Def of Straight Angles
4. Angle Addition Postulate
5. Substitution
6. 2 ll Lines, Alt Int Angles Congruent
7. Substitution Property
1 2 3 180
m m m
      
||
DE AC
DE
B
C
A
2
1 3
180
m DBE
  
4 2 5
m DBE m m m
      
D E
4 5
4 2 5 180
m m m
      
1 4; 3 5
m m m m
     
1 2 3 180
m m m
      
∆ ABC

10. How can we use this?
• The ladder is leaning
on the ground at a
75º angle. At what
angle is the top of the
ladder touching the
building?
75
75 90 180
165 180
15
x
x
x
  
 

15

11. Find the missing angle.
43
47

12. Find the value of X.
30° X-8
2x+28
X-8 + 2x+28 + 30 = 180°
3x + 50 = 180
3x = 130
X = 43.33°

13. Find the missing angles.
55° 25°
y°
w° x°
120°
W = 35°
X = 35°
Y = 120°

14. Exterior Angle Theorem
An exterior angle of a triangle…
… is equal in measure to the sum of the
measures of its two remote interior angles.
Exterior
Remote Interior
Adjacent Interior
( An exterior angle and its adjacent interior angle are supplementary )

15. Given: ∆ ABC with exterior
Prove:
1. ABC is a triangle
with exterior angle
4.
2.
3.
4.
5.
6.
7.
1. Given
2. Straight Angle Postulate
3. Angle Addition Postulate
4. Substitution
5. Triangle Sum Theorem
6. Substitution Property
7. Subtraction Prop. Of
Equality
4 1 2
m m m
    
180
m BCD
  
C
D
3 4
m BCD m m
    
3 4 180
m m
    
1 2 3 180
m m m
      
3 4 1 2 3
m m m m m
        
4 1 2
m m m
    
4

A
B
2
1
3 4

16. Find the missing angles’
measurements (<1 and <2).
120º
55º 35
2 1
remote
interior
angles
< 1 = 90 + 55
< 2 = 120 + 35

17. For Warm-up
70°
y°
z° w°
D E
50° x°
(x-30)°
x°
70°
60°
50° 110°
D E
50° 70°
(80-30)°
80°
3X – 60 = 180
>
>

18. 1
3
2 59°
47°
64°
1
2
3
28°
46°
55°