4.1 Triangles and Angles4.1 Triangles and Angles

Interior and Exterior AnglesInterior and Exterior Angles

Types of TrianglesTypes of Triangles

Definition of a triangle

A triangle is three segments joined at three noncollinear end points.

vertex

vertex

vertex

side side

side

sidesadjacent

Types of Triangles by Sides

3 Sides congruent → Equilateral

Types of Triangles by Sides

2 Sides congruent → Isosceles

Part of the Isosceles

Triangle

leg leg

base

Types of Triangles by Sides

No Sides congruent → Scalene

Types of Triangles by Sides

3 Sides congruent → Equilateral

2 Sides congruent → Isosceles

No Sides congruent → Scalene

Types of Triangle by Angles

All Angles less than 90 degrees → Acute

Types of Triangle by Angles

One Angle greater

than 90 degrees → Obtuse

Types of Triangle by Angles

One Angle equal to 90 degrees → Right

Parts of the Right Triangle

Across from the right angle is the hypotenuse.

hypotenuse

leg

leg

Equiangluar

All the angles are Equal

Interior Angles vs. Exterior Angles

Interior Angles in Pink

Exterior Angles

In light green

A Theorem about Angles in a Triangle

The interior angles in a triangle add to 180º

Solve for x

25

110

x

Theorem about an exterior angle

The measure of an exterior angle equals the measure of the two nonadjecent interior angles.

57

86

1438657

Solve for x

14

79

x

Corollary for the fact that interior angles add to 180º

The acute angles of a Right triangle are complementary.

x

x90

HomeworkHomework

Page 198 - 201 Page 198 - 201

# 10 - 15,# 10 - 15,

16 - 38 even,16 - 38 even,

42, 49, 5042, 49, 50

HomeworkHomework

Page 198 - 201 Page 198 - 201

# 17 – 43 odd, # 17 – 43 odd,

45 – 47, 45 – 47,

52 - 6852 - 68