What Is a Triangle? Key Vocabulary
A triangle is a closed, three-sided polygon. Before diving into triangle properties, let's lock down the vocabulary you'll need throughout this subtopic.
A corner point of a triangle where two sides meet. A triangle has exactly three vertices (plural of vertex).
An angle formed inside a triangle between two of its sides. Every triangle has exactly three interior angles.
An angle formed outside a triangle when one side is extended beyond a vertex. It sits adjacent to (next to) one interior angle.
A triangle in which all three sides have different lengths and all three angles are different.
A triangle in which two sides are equal in length. The equal sides are called the legs, the unequal side is the base, and the two angles sitting on the base are the base angles.
A triangle in which all three sides are equal in length. All three interior angles are equal, each measuring 60°.
In an isosceles triangle, the apex is the vertex where the two equal sides meet — it sits directly opposite the base.
Think of an isosceles triangle like a tent: two equal sloping sides meet at the top (apex), and the ground forms the base. The base angles are where the tent poles meet the ground — they're always equal by symmetry.
Angle Sum of a Triangle
One of the most fundamental facts in geometry is this:
The sum of the three interior angles of any triangle is always 180°.
If the three interior angles are , , and , then:
This works for every triangle — scalene, isosceles, equilateral, right-angled — no exceptions.
Example 1: A triangle has angles 47° and 68°. Find the third angle.
Step 1: Write the equation.
Step 2: Simplify.
Step 3: Solve.
The third angle is 65°.
Example 2: An isosceles triangle has a base angle of 52°. Find all three angles.
Because it's isosceles, both base angles are equal, so two angles are 52° each.
The three angles are 52°, 52°, and 76°.
Students sometimes assume that only right-angled or isosceles triangles have angles summing to 180°. The rule applies to all triangles — no exceptions!
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