Classify triangles

Learning Objectives Define a triangle and its basic components (vertices, sides, angles). Classify triangles as equilateral, isosceles, or scalene based on their side lengths. Classify triangles as acute, right, or obtuse based on their angle measures. Apply the Triangle Sum Theorem to find unknown angle measures in a triangle. Classify a triangle by both its side lengths and angle measures given sufficient information. Solve problems involving the classification of triangles in various contexts. Ever wondered how builders or artists decide which triangular shapes to use in their designs? 📐 Let's uncover the secrets behind classifying these fundamental figures! In this lesson, you'll learn how to categorize triangles based on their side lengths and angle measures...

TermDefinitionExample TriangleA polygon with three sides and three interior angles.A road sign shaped like a yield sign is a triangle. Vertex (plural: Vertices)A point where two sides of a polygon meet. A triangle has three vertices.In triangle ABC, points A, B, and C are the vertices. Side LengthThe measure of a segment forming one of the three sides of a triangle.A triangle with sides measuring 3 cm, 4 cm, and 5 cm. Angle MeasureThe measure of an interior angle formed by two sides of a triangle.A triangle with angles measuring 30°, 60°, and 90°. Acute AngleAn angle that measures less than 90 degrees.An angle measuring 45° is an acute angle. Right AngleAn angle that measures exactly 90 degrees, often indicated by a square symbol.The corner of a square or a book forms a right angle. Obtus...

Triangle Sum Theorem $\angle A + \angle B + \angle C = 180^\circ$ The sum of the measures of the three interior angles of any triangle is always 180 degrees. This rule is fundamental for finding unknown angles. Classification by Side Lengths 1. **Equilateral Triangle:** All three sides are equal in length. (Implies all three angles are equal, $60^\circ$ each) 2. **Isosceles Triangle:** At least two sides are equal in length. (Implies the angles opposite the equal sides are also equal) 3. **Scalene Triangle:** All three sides have different lengths. To classify a triangle by its sides, compare the lengths of its three sides. The number of equal sides determines its classification. Classification by Angle Measures 1. **Acute Triangle:** All three interior angles are acut...