A Triangle

• Is a figure formed by three segments

• Joining three noncollinear points….it has

• Sides…..

• And Angles.

ABC

C

B

A

Triangles can be classified by sides..

• Scalene (no sides equal)

• Isosceles (as least 2 sides equal)

• Equilateral (3 congruent sides) JKL

DEF

ABC

L

KJ

F

ED

C

B

A

A

A Triangle can be classified by ANGLES…

• Acute (3 acute angles)

• Right (1 right angle)

• Obtuse (1 obtuse angle)

• Equiangular (3 congruent angles)

Triangle Vocabulary

• Vertex A

• Vertex B

• Vertex C

C

AB

Triangle Vocabulary

• Side opposite angle A

• Side opposite angle B

• Side opposite angle C

C

AB

Right Triangles

• Hypotenuse

• Leg

• Leg

C

AB

Isosceles Triangle

• Base

• Leg

• Leg

C

A

B

When the sides of a triangle are extended….the triangle has

• Interior Angles

• Exterior AnglesExteriorAngle

ExteriorAngle

ExteriorAngle

InteriorAngles

C

A

B

Classify the triangle by it’s SIDES and Angles.

Classify the triangle by it’s SIDES and Angles.

Classify the triangle by it’s SIDES and Angles.

Classify the triangle by it’s SIDES and Angles.

Classify the triangle by it’s SIDES and Angles.

Classify the triangle by it’s SIDES and Angles.

Complete each sentence with the word always, sometimes or

never.

Click here to explore

Click here to explore

Theorem 4.1-Triangle Sum Theorem

• The sum of the interior angles of a triangle is 180 degrees.

mABC+mDEF+mGHI = 180

mGHI = 42mDEF = 32mABC = 106

B

E

A

C

GI

D

F

What is the measure of the numbered angle?

What is the measure of the numbered angle?

What is the measure of the numbered angle?

Theorem 4.2-Exterior Angle Theorem

• The measure of an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles.

mDEF+mGHI = 142

mGHI = 73

mDEF = 68

mCBA = 142

E

H

BG

I

FD

CA

A corollary to a theorem

• Is a statement that can be proved easily using a theorem

• Think of it as a mini-theorem.

Corollary to the triangle sum theorem

• The acute angles of a right triangle are complementary. C

BA

Assignment 4.1