Types of triangles

Learning Objectives Classify triangles by their side lengths (equilateral, isosceles, scalene). Classify triangles by their angle measures (acute, right, obtuse, equiangular). Combine side and angle classifications to describe a triangle completely (e.g., right isosceles). Apply the Triangle Angle-Sum Theorem to find the measure of a missing angle. Use the Triangle Inequality Theorem to determine if three given side lengths can form a valid triangle. Use the properties of isosceles and equilateral triangles to find missing side lengths and angles. Ever wonder how the strong, triangular shapes in bridges and buildings are designed? 🏗️ It all starts with understanding their basic types! In this tutorial, we will explore the different ways to classify triangles using their sid...

TermDefinitionExample Classification by SidesCategorizing triangles based on the lengths of their three sides.An Equilateral triangle has 3 equal sides, an Isosceles triangle has at least 2 equal sides, and a Scalene triangle has no equal sides. Classification by AnglesCategorizing triangles based on the measures of their three interior angles.An Acute triangle has all angles < 90°, a Right triangle has one 90° angle, and an Obtuse triangle has one angle > 90°. Equilateral TriangleA triangle with three congruent (equal length) sides. It is also equiangular, meaning all three angles are 60°.A triangle with side lengths of 5 cm, 5 cm, and 5 cm. Isosceles TriangleA triangle with at least two congruent sides. The angles opposite the congruent sides (called base angles) are also congruen...

Triangle Angle-Sum Theorem m∠A + m∠B + m∠C = 180° The sum of the measures of the three interior angles of any triangle is always 180 degrees. Use this to find a missing angle when you know the other two. Triangle Inequality Theorem a + b > c, a + c > b, and b + c > a The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Use this to check if three given side lengths can form a triangle. Isosceles Triangle Theorem If two sides are congruent, the angles opposite them are congruent. In an isosceles triangle, if you know two sides are equal, you also know the angles across from them are equal. This helps find missing angle measures.