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What Is the Triangles?(With Examples)

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).

Grades 4-8Key Stage 2-3Årskurs 4-8Klasse 5-8

📖Definition

📐Formula

Angle sum: A + B + C = 180°; Area: A = ½ × base × height

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°.

∠A + ∠B + ∠C = 180°

Apply Triangle Inequality

The sum of any two sides must be greater than the third side.

a + b > c (for all combinations)

⚠️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

Easy

A triangle has sides of 5 cm, 5 cm, and 5 cm. What type is it?

Answer: Equilateral triangle

Medium

A triangle has angles of 30° and 60°. Find the third angle and classify by angles.

Answer: 90°, Right triangle

Hard

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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Angles Pythagorean Theorem Area Congruent Triangles

Curriculum Alignment

CommonCore (4.G.A.2)KS3KMK

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