G Triangle Theorems
 
 
 
 

The sum of the angles for any triangle is 180 degrees.

If we know two angles, we can total and subtract from

180 to get the missing angle.  Find the missing angle

measurement.

23
o
o

39

o

  180

 - 62

  118

   39

+ 23

   62 
 
 

The sum of the angles for any triangle is 180 degrees.

If we know two angles, we can total and subtract from

180 to get the missing angle.  Find the missing angle

measurement.

o

63

o

77

o
 
 

The sum of the angles for any triangle is 180 degrees.

If we know two angles, we can total and subtract from

180 to get the missing angle.  Find the missing angle

measurement.

o

50

90

o
o
 
 

The longest side of a triangle is always directly across

from the largest angle.  The shortest side of the triangle

is always directly across from the smallest angle.   The

medium side is directly across from the medium angle.  

Name the longest side.

23
o

z

118

o

y

x

39

o

 side x

 side y

 side z

 
 

The longest side of a triangle is always directly across

from the largest angle.  The shortest side of the triangle

is always directly across from the smallest angle.   The

medium side is directly across from the medium angle.  

Name the longest side.

53

o

z

x

60

o

y

67

o

 side x

 side y

 side z

 
 

The longest side of a triangle is always directly across

from the largest angle.  The shortest side of the triangle

is always directly across from the smallest angle.   The

medium side is directly across from the medium angle.  

Name the longest side.

53

o

z

x

60

o

y

67

o

 side x

 side y

 side z

 
 

The longest side of a triangle is always directly across

from the largest angle.  The shortest side of the triangle

is always directly across from the smallest angle.   The

medium side is directly across from the medium angle.  

Name the longest side.

53

o

z

x

42

o

85

y

o

 side x

 side y

 side z

 
 

The longest side of a triangle is always directly across

from the largest angle.  The shortest side of the triangle

is always directly across from the smallest angle.   The

medium side is directly across from the medium angle.  

Name the longest side.

42

o

z

x

85

53

y

o
o

 side x

 side y

 side z

If three in a row angle, side, angle  OR side, angle, side,

a unique triangle is created.

 

 

If the three sides are known, a unique triangle is created.

 

 

If the three angles are known, then multiple, similar

triangles are created.

Will knowing two sides of a triangle be a unique or

multiple possibilities type triangle?

 

multiple possibilities
unique (only one triangle can be made)

Will knowing two angles of a triangle be a unique or

multiple possibilities type triangle?

 

multiple similar
unique

Will knowing three sides of a triangle be a unique or

multiple possibilities type triangle?

 

multiple possibilities
unique

Will knowing two sides of a triangle and the connecting

angle be a unique or multiple possibilities type triangle?

 

unique
multiple possibilities

Will knowing two sides of a triangle and an angle but

not the location of the angle be a unique or multiple

possibilities type triangle?

 

unique
multiple possibilities

Will knowing two angles of a triangle and the connecting

side be a unique or multiple possibilities type triangle?

 

unique
multiple possibilities

Will knowing two angles of a triangle and a side but not

the location of the side be a unique or multiple

possibilities type triangle?

 

unique
multiple possibilities
 
 
 
 
 
 
 
 
 
 
 
 

Theorem:  A measure of an exterior angle of a triangle

is equal to the sum of the measures of the two non-

adjacent interior angles.

 Exterior Angles of Triangles

(77 + 90)

o

13

o

77

90
o
o
 
 
o
103

51

o
o
 
 
o

92

o

65

o
 
 
o

89

o

74

o
 
 

16

o

92

o
o
 
 

15

o

88

o
o
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