TRIANGLES

Triangle• A triangle is a two-

dimensional (flat) 3-sided shape.

Classifying Triangles by

Angle• You can classify

triangles by the measurement of their interior angles.

• If a triangle has one 90° angle, it is called a right triangle.• If a triangle has one obtuse angle, it is called an obtuse triangle.• If a triangle has three acute angles, it is called an acute triangle.

Right Triangles• A right triangle must have

one angle that measures 90° exactly. 90°

• An obtuse triangle must have one angle that is greater than 90°.

Obtuse Triangles

• An acute triangle has 3 acute angles. Each angle must measure less than 90°.

Acute Triangles

What kind of sign is this? What kind of

triangle?

Classifying Triangles by

Length• You can classify

triangles by the side lengths and angle measurements.

• If a triangle has 3 equal side lengths, it is called an equilateral triangle.

• If a triangle has 2 equal side lengths, it is called an isosceles triangle.

• If a triangle has no equal side lengths, it is called a scalene triangle.

Equilateral Triangles

• Equilateral triangles are made up of three equal side lengths and three 60° angles. It has three lines of symmetry.

3 ft

3 ft

3 ft

60°

60°60°

• Isosceles triangles are made up of two equal side lengths and two equal angles. It has one line of symmetry.

Isosceles Triangles

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• Scalene triangles are made up of 3 side lengths and 3 angles that are all different sizes and measurements. It does not have any lines of symmetry.

Scalene Triangles

Angles of Elevation• The angle of elevation is the

angle between the horizontal line of sight and the line of sight up to an object. For example, if you are standing on the ground looking up at the top of a mountain, you could measure the angle of elevation.

• The angle of depression is the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, looking down at an object, you could measure the angle of depression.

Angles of Depression

Importance of Trigonometry