What is a triangle?

Triangles can be classified by their angles. There are four different classifications by angles.

Equiangular triangles are triangles with three congruent angles.

Acute triangles are triangles with three acute angles.

Obtuse triangles are triangles with one obtuse angle and two acute angles.

Right triangles are triangles with one right angle and two acute angles.

WHITE NOTE CARD

Triangle Classification by Angles

Equiangular - three congruent angles

Acute Obtuse Right

3 acute angles 1 obtuse angleand 2 acuteangles

1 right angle and 2 acute angles

Triangles can also be classified by their sides.

What is an equilateral triangle?

• 3 congruent sides

• 3 acute angles

• 3 congruent angles

Triangles can also be classified by their sides in three differentways.

What is an isosceles triangle?

• 2 congruent sides

• could be acute, right, or obtuse

• 2 congruent angles

There are three ways to classify triangles by sides.

What is a scalene triangle?

• no congruent sides

• could be acute, right, or obtuse

• no congruent angles

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Triangle Classification by Sides

Equilateral Isosceles Scalene

3 congruent sides

3 congruent angles

Acute triangle

2 congruent sides

2 congruent angles

Acute, right, or obtuse

No congruent sides

No congruent angles

Acute, right or obtuse

Angle Sum Theorem

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

Prove that the sum of the angles in a triangle is 180º.

º

Note card

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.

4 + 2 + 5 = 180

COLORED NOTE CARD

Angle Sum Theorem

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

The Parallel Postulate

If you are given a line and a point not on the line, there is exactly one line that can be drawn through the point that is parallel to the line.

A

B

C

You can draw this line because it does not change the given information.

A

B

C1

2

3

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