What Is a Triangle?
A triangle is one of the most fundamental shapes in geometry. It is a closed, flat shape with three straight sides, three corners (called vertices), and three interior angles.
Triangles appear everywhere — in roof structures, bridge designs, musical instruments, and even slices of pizza!
A polygon with exactly three sides and three interior angles. The word comes from Latin: tri (three) + angulus (angle).
An angle formed inside a triangle at each vertex, between two sides of the triangle.
Think of a triangle like a three-legged stool — it is the most stable shape because no matter what size or style, it always holds its structure. This is partly why architects and engineers love triangles!
The Angle Sum Property of Triangles
Here is one of the most important rules in geometry:
The three interior angles of any triangle always add up to exactly 180°.
This is true for every triangle — big, small, skinny, wide — no exceptions!
Worked Example 1: A triangle has angles of 60°, 70°, and an unknown angle. Find the missing angle.
Step 1: Write the angle sum equation:
Step 2: Add the known angles:
Step 3: Subtract from 180°:
The missing angle is 50°.
To find a missing angle in a triangle, simply add the two known angles and subtract from 180°. You can always use this shortcut!
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