Goal, to classify triangles by their sides and by their angles.

GEOMETRY - CLASSIFYING TRIANGLES

Equilateral triangle,

3 congruent sides.

Isosceles triangle,

at least 2 congruent sides

Scalene triangle,

no congruent sides.

GEOMETRY - CLASSIFYING TRIANGLES

Classification of triangles by SIDES Classification of triangles by SIDES

Equiangular Triangle; 3 congruent angles Acute Triangle;

3 acute angles

Classification of triangles by ANGLES Classification of triangles by ANGLES

Right triangle; 1 right angle

Obtuse triangle; 1 obtuse angle

GEOMETRY - CLASSIFYING TRIANGLES

GEOMETRY - CLASSIFYING TRIANGLES

The angles that are adjacent to the interior angles are the exterior angles.

1

3

2

The three angles of a triangle are called the

INTERIOR ANGLES

interior

angles

When the sides of a triangle are extended, other angles are formed.

GEOMETRY - INTERIOR & EXTERIOR ANGLES

A

B

C

The sum of the measures of the angles of a triangle is 180°.

m + m + m = 180°

AC

B

A

B

GEOMETRY - TRIANGLE SUM THEOREM

C

Corollary to the Triangle Sum TheoremCorollary to the Triangle Sum Theorem

The acute angles of a right triangle are complementary.

mA + mB = 90°.

AB

C

GEOMETRY - TRIANGLE SUM THEOREM

Exterior Angle Exterior Angle

A

B

1

GEOMETRY - TRIANGLES

C

Exterior angle

12060

The exterior angle and the adjacent interior angle are supplementary.

Exterior Angle Theorem Exterior Angle Theorem

A

B

GEOMETRY - TRIANGLES

C 1305030

100100

30 130

+ =

Exterior Angle Theorem Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles (remote interior angles).

mA + mB = m1

A

B

1

GEOMETRY - TRIANGLES

C

55

46

?

Triangle Sum Theorem(1)

79

GEOMETRY - TRIANGLES

x+5

3x

15

(2)(x+5)+3x+15 = 180

4x+20 = 180

4x = 160

x = 40

GEOMETRY - TRIANGLES

161 73

?(3)

GEOMETRY - TRIANGLES

19

92

11663

x?

(4)

25 35

y?

GEOMETRY - TRIANGLES

91 119