A triangle can be classified by _________ and __________.sides angles

There are four ways to classify triangles by angles. They are

EquiangularAcuteObtuseRight

All angles congruent3 acute angles1 obtuse and two acute angles1 right and two acute angles

There are three ways to classify triangles by sides. They are

Equilateral - 3 congruent sides and anglesIsosceles - 2 congruent sides and anglesScalene - no congruent sides or angles

Let’s take a closer look at the isosceles triangle:

The two congruent sides are called legs.

LEG LEG

The other side is called the base.

BASE

The two congruent angles are called the base angles.

The other angle is called the vertex angle.

VERTEX ANGLE

BASE ANGLES

WHITE NOTE CARD:

Isosceles Triangle

LEG LEG

BASE

VERTEX ANGLE

BASE ANGLES

The legs and base angles are congruent.

Vertex angles is always opposite the base.

REVIEW:

RIGHT TRIANGLE

LEG

LEG

HYPOTENUSE

Angle Sum Theorem

What is the sum of the measures of the angles in a triangle?

Is this true for all triangles? Even the really big ones and really small ones?

Proof of Angle Sum Theorem

Remember the proof of the Triangle Sum Theorem? Good stuff!

Given: ABC is a triangle.

A

B

C

(Number the angles for convenience)

1

2

3

Prove: 1 + 2 + 3 = 180

STATEMENTS REASONS

1. ABC is a triangle 1. Given

2. Draw a line through B that is parallel to AC

2. Parallel Postulate

3. 4 + 2 + 5 = 180

4. 1 4 and 3 5

5. 1 + 2 + 3 = 180

4. If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

5. Substitution Property

4 5

3. Definition of Supplementary angles

Click on the reasonfor an explanation.

An exterior angle is formed by one side of a triangle and the extension of another side.

Exterior angle

Exterior angle

Exterior angle

Interior angles

Remote interior angles are the interior angles in the triangle that are not adjacent to the exterior angle.

Exterior angle

remote interior angles

Exterior angle

Exterior angle

Exterior Angle Theorem

The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.

Exterior angle

Remote interior angles

41

2

In other words, 4 = 1 + 2.

Add this proof to page 37 that already has the Triangle Sum Theorem proof.

What could be more fun than

another proof? I can’t wait!

Given: ABC is a triangle with exterior angle 4

A

B

C

1

2

3 4

Prove: 1 + 2 = 4

(The sum of the measures of the two remote interior angles in a triangle is equalto the measure of the exterior angle)

STATEMENTS REASONS

1. ABC is a triangle with exterior angle 4

2. 1 + 2 + 3 = 180

3. 3 + 4 = 180

4. 1 + 2 + 3 = 3 + 4

5. 1 + 2 = 4

1. Given

2. Triangle Sum Theorem

3. Definition of Linear Pair

4. Substitution Property

5. Subtraction Property

1 + 2 + 3 = 180

Add the Exterior Angle Theorem to your Triangle Sum Theorem note card (it’s a colored one).

Triangle Sum Theorem

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

Exterior Angle Theorem

The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles.

4

2

1

4 = 1 + 2

Proofs are awesome! I

hope we get to do more of them

soon!

I’m sure we will!

Geometry is super!

I love math! It’s

everywhere!