Acute, obtuse, and right triangles

Learning Objectives Define acute, obtuse, and right triangles based on their angle measures. Apply the Triangle Angle-Sum Theorem to determine a missing angle measure. Identify the legs and hypotenuse of a right triangle. Use the Pythagorean Theorem to find an unknown side length in a right triangle. Apply the Converse of the Pythagorean Theorem to classify a triangle as acute, obtuse, or right, given its three side lengths. Solve real-world problems involving the classification and properties of triangles. Ever wondered how a carpenter ensures a corner is perfectly square or how an architect designs a stable roof? 📐 It all comes down to the simple, powerful geometry of triangles! In this tutorial, we will explore the three main types of triangles based on their angles: ac...

TermDefinitionExample Acute TriangleA triangle in which all three interior angles are acute (measure less than 90°).A triangle with angles measuring 60°, 70°, and 50° is an acute triangle. Obtuse TriangleA triangle that has one obtuse angle (an angle measuring more than 90°). A triangle can only have one obtuse angle.A triangle with angles measuring 110°, 40°, and 30° is an obtuse triangle. Right TriangleA triangle that has one right angle (an angle measuring exactly 90°).A triangle with angles measuring 90°, 45°, and 45° is a right triangle. Legs (of a Right Triangle)The two sides of a right triangle that form the 90° angle.In a right triangle with sides 3, 4, and 5, the sides with lengths 3 and 4 are the legs. HypotenuseThe side opposite the right angle in a right triangle. It is always...

Pythagorean Theorem a^2 + b^2 = c^2 Use this formula for any RIGHT triangle to find the length of a missing side. Here, 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse. Converse of the Pythagorean Theorem Given a triangle with side lengths a, b, and c, where c is the longest side: 1. If c^2 < a^2 + b^2, the triangle is ACUTE. 2. If c^2 > a^2 + b^2, the triangle is OBTUSE. 3. If c^2 = a^2 + b^2, the triangle is RIGHT. Use this set of rules to classify a triangle as acute, obtuse, or right when you only know the lengths of its three sides. Always identify 'c' as the longest side before you begin.