Two-Dimensional Figures

Classifying Triangles#

A triangle is a polygon with three sides and three angles. Triangles can be classified in two ways: by their angle measures or by their side lengths.

Classifying by Angles#

Acute triangle: All three angles are less than 90°.

• Example: An equilateral triangle (all angles equal 60°)

Right triangle: One angle is exactly 90°.

• The side opposite the right angle is called the hypotenuse (the longest side)
• Example: A triangle with angles of 90°, 45°, and 45°

Obtuse triangle: One angle is greater than 90°.

• Example: A very flat, wide triangle with one large angle

Classifying by Side Lengths#

Equilateral triangle: All three sides are equal in length. (All angles also equal 60°.)

Isosceles triangle: Exactly two sides are equal in length. (The two base angles are also equal.)

Scalene triangle: All three sides are different lengths. (All three angles are also different.)

Combining Classifications#

A triangle can have two classifications:

• A right isosceles triangle (one 90° angle, two equal sides)
• An acute scalene triangle (all angles < 90°, all sides different)

Triangle Properties#

• The sum of all three angles always equals 180°
• The longest side is always opposite the largest angle
• No triangle can have two right angles or two obtuse angles (it would exceed 180°)

Drawing Triangles#

When drawing a specific triangle, start with the known angles or side lengths. For a right triangle, draw the right angle first with a small square, then add the other two sides.