📖Definition
A triangle is a polygon with three sides, three angles, and three vertices. The sum of the interior angles always equals 180°. Triangles can be classified by their sides (equilateral, isosceles, scalene) or by their angles (acute, right, obtuse).
📐Formula
All triangles have angles that add up to 180°. Equilateral triangles have three equal sides and three 60° angles. Isosceles have two equal sides. Scalene have no equal sides.
📝Step-by-Step Guide
Classify by Sides
Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides.
Classify by Angles
Acute: all angles < 90°. Right: one 90° angle. Obtuse: one angle > 90°.
Use the Angle Sum Property
The three interior angles always sum to 180°.
Apply Triangle Inequality
The sum of any two sides must be greater than the third side.
⚠️Common Mistakes to Avoid
- Forgetting that angles must sum to 180°
- Confusing equilateral with isosceles
- Not checking if three lengths can form a triangle
- Mixing up classification by sides vs by angles
- Using the wrong height when calculating area
✏️Practice Problems
A triangle has sides of 5 cm, 5 cm, and 5 cm. What type is it?
Answer: Equilateral triangle
A triangle has angles of 30° and 60°. Find the third angle and classify by angles.
Answer: 90°, Right triangle
Can a triangle have sides of length 3, 4, and 8?
Answer: No, because 3 + 4 = 7 < 8 (fails triangle inequality)
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