A triangle is a closed figure with 3 sides and 3 angles.

The three angles always add to 180°

Triangles can be classified by the size of their angles:

Acute Triangle: all angles acute     (less than 90 degrees)







Right Triangle: Has one angle equal to 90 degrees.  The right-angle symbol is a small square.







Obtuse Triangle: Has an angle more than 90 degrees









Triangles can be classified by the length of their sides:

Scalene Triangle: A triangle with all sides of different length







Isosceles Triangle: A triangle with two sides equal








Equilateral Triangle: A triangle with all sides equal







Similar Triangles: have the same shape, but the size may be different.  (“~” means ” is “similar to”)

Corresponding sides of similar triangles are in proportion (SCALE), and corresponding angles of similar triangles are congruent (equal value).




We denote which angles are congruent with the same number of curved lines.

Congruent Triangles: have the same shape and size. (“” means “is congruent to”)






Two polygons are congruent if one can be transformed into the other by translation, rotation, and/or reflection.

An Interior Angle is an angle inside the triangle. An exterior angle is an angle formed by one side of a triangle and a line extended from an adjacent side.


We may observe that they are a pair of supplementary angles (the measure of the interior angle plus the measure of the exterior equals 180 degrees).

Also, we may observe that the measure of the exterior angle equals the sum of the other two interior angles of the triangle (Exterior Angle Theorem).


Classifying Triangles by Side

Triangle Types by Angle

Triangle Properties

Classifying Triangles by sides:

Equilateral triangle: 3 congruent sides

Isosceles Triangle: 2 congruent sides

Scalene Triangle: No congruent sides

Classification of triangles:









Triangle Classification: (regarding its angles)

Acute: (all angles are acute [angle<90°])

Right: (one angle is right [angle=90°])

Obtuse: (one angle is obtuse [angle>90°])

Equiangular: (all angles are equal)


Acute triangles:







Right Triangles:

In a right triangle, one of the angles measures 90 degrees. This angle is represented by a small square.

The side opposite the right angle is the largest and is called hypotenuse.

The contiguous sides of the right angle are called legs.







Obtuse Triangles:








Pythagorean theorem

In a right triangle (a triangle with one right angle ), the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

GE29  Pythagoras