Classify triangles

Learning Objectives Classify any triangle by its side lengths as scalene, isosceles, or equilateral. Classify any triangle by its interior angles as acute, right, obtuse, or equiangular. Apply the Triangle Sum Theorem to find unknown angle measures. Use the Exterior Angle Theorem to solve for unknown angles. Solve algebraic equations involving side lengths and angle measures to classify triangles. Determine the possible classifications of a triangle given partial information. Have you ever wondered why the pyramids in Egypt, the sails on a boat, and the trusses of a bridge are all made of triangles? 🔺 Let's find out why this simple shape is so powerful! This tutorial will teach you the two primary ways to classify triangles: by their side lengths and by their angle me...

TermDefinitionExample Classification by SidesGrouping triangles based on the lengths of their three sides.A triangle with side lengths 5 cm, 5 cm, and 7 cm is Isosceles because two sides are equal. Classification by AnglesGrouping triangles based on the measures of their three interior angles.A triangle with angles 40°, 60°, and 80° is an Acute Triangle because all angles are less than 90°. Scalene TriangleA triangle with no congruent (equal length) sides.Side lengths: 3, 4, 5 Isosceles TriangleA triangle with at least two congruent sides. The angles opposite the congruent sides are also congruent.Side lengths: 7, 7, 10 Equilateral TriangleA triangle with all three sides congruent. It is also equiangular, meaning all three angles are 60°.Side lengths: 6, 6, 6 Acute, Right, and Obtuse Tria...

Triangle Sum Theorem The sum of the measures of the interior angles of any triangle is always 180 degrees. Formula: `m\angle A + m\angle B + m\angle C = 180^\circ` Use this rule when you know two angles in a triangle and need to find the third. It's also essential for setting up algebraic equations when angles are given as expressions. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. Formula: `m\angle_{exterior} = m\angle_{remote1} + m\angle_{remote2}` Use this when you need to find the measure of an angle outside the triangle or to relate an exterior angle to the two opposite interior angles, often in problems with variables.