Types of TrianglesAnd Angle Sum Theorems

Notation for sides. AB CB AC Angles ABC or B Vertex angle Base angle Opposite side Opposite angle

A

B C

Equilateral Triangle : all sides and angles are congruent. ( Equiangular Triangle)

9

9

9

At least two sides and two angles are congruent.

10 10

4

Vertex

Base Angles

None of the sides or angles are congruent

8

11

4

m∠A + m∠B + m∠C = 180 degrees

A

B

C

Find the value of the unknown angle.

87 °44 °

x°

180 ° – 87 ° – 44 ° = Unknown angle X

= 49 °

X° + 87° + 44° = 180°

m∠ A = (2x – 3)° , m∠ B = (x + 5)° , and m∠ C = (x + 8)°

C B

A

Solution

m∠A + m∠B = m∠E The sum of the remote interior angles equal

the value of the exterior angle.

A B

E exterior angle

remote interior angle

56°

88°

E°

56° + 88° = the unknown exterior angle

= 144 degrees

All angles are congruent. They are each 60 degrees. (Equilateral Triangle)

60°

60°

60°

61°

38°

X° Y°

Z°

26°

180° – 38° – 61° = 81° X° 61° + 38° = 99° Y°

180° – 26° – 99° = 55° Z°

122 °

18 °

T° V° K°

R°

Solution

P°