Introduction to Angles and Triangles.

I can identify the properties of angles and triangles.

Definitions• Complementary Angle- Two angles whose sum equals 90 degrees.

• Supplementary Angle- Two angles whose sum equals 180 degrees.

• Vertical Angle-A pair of opposite congruent angles formed by intersecting lines.

• Congruent- Having the same size and shape, the symbol for congruent is ≅.

• Congruent Angles- Angles that have the same measure.

• Acute Angle-An angle that measures more than 0∘ and less than 90∘

• Acute Triangle- A triangle where all three angles measure less than 90∘

Definitions Continued• Obtuse Angle-An angle that measures more than more than 90∘ but less than 180∘

• Obtuse Triangle- A triangle containing ONE obtuse angle.

• Right angle- An angle that measures exactly 90∘

• Right Triangle- A triangle with a 90∘ angle.

• Scalene Triangle- A triangle with no congruent sides or angles.

• Isosceles Triangle- A triangle with two congruent sides and angles.

• Adjacent Angles- Angles in the same plane that have a common vertex and side.

• Vertex- On an angle or polygon, the point where the two sides intersect.

Complementary Angle

Supplementary Angles

Vertical Angle

Vertical angles are opposite one another.

75º

75º

105º105º

Vertical angles are opposite one another.

75º

75º

105º105º

Two angles that have the same measure are called congruent angles.

Congruent angles have the same size and shape.

A

BC

300

D

EF

300

D

EF

300

Congruent Angles

Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.

Types of Angles

A

right angle m A = 90

acute angle 0 < m A < 90

A

obtuse angle 90 < m A < 180

A

Angle Measure

What is a triangle?• A triangle is a closed geometrical shape with three vertices(points).

• The sum of all angles INSIDE a triangle is 180∘

60∘

60∘ 60∘

Types of Triangles• Equilateral triangle: A triangle with three congruent (equal) sides and three

equal angles

These marks indicate equality.

Types of Triangles• Isosceles triangle: A triangle with at least two congruent (equal) sides

Types of Triangles• Right triangle: Has only one right angle (90 degrees)

This box indicates a right angle or a 90-degree angle.

Types of Triangles• Scalene triangle: A triangle that has no congruent (equal) sides

Types of Triangles• Name each type of triangle

1

2

3

4

Types of Triangles• Name each type of triangle

1

2

3

4

Equilateral

Right

Isosceles

Scalene