Lesson 20: Triangles

New Concept

This course bridges arithmetic with algebra and geometry. You will master core skills and apply them to solve increasingly complex and interesting real-world problems.

What’s next

This lesson begins our journey into geometry. We will start by classifying different types of triangles and then learn how to calculate their area.

Property

A triangle is a polygon with three sides. Triangles are classified by their angles and by their side lengths:

• By Angles: Acute (all angles < 90°), Right (one 90° angle), Obtuse (one angle > 90°).
• By Sides: Equilateral (3 equal sides), Isosceles (at least 2 equal sides), Scalene (0 equal sides).

Examples

• A triangle with a 90° angle and sides of 3 cm, 4 cm, and 5 cm is a right scalene triangle.
• A triangle with three 60° angles and all sides equal is an acute equilateral triangle.
• A triangle with angles 40°, 40°, 100° is an obtuse isosceles triangle.

Explanation

Property

The sum of the angle measures in any triangle is always $180^\circ$.

Examples

• In a right triangle, one angle is $90^\circ$. If another angle is $50^\circ$, the third is $180^\circ - 90^\circ - 50^\circ = 40^\circ$.
• An isosceles triangle has two equal base angles of $70^\circ$. The third angle is $180^\circ - (70^\circ + 70^\circ) = 40^\circ$.

Explanation

A triangle’s three angles are locked in a pact to always add up to exactly 180 degrees. It's the ultimate rule! This means if you know two of the angles, you can become a math detective and easily figure out the third. It's the secret key to solving for missing angles in any triangle you find.