Hypotenuse-Leg Theorem

Learning Objectives Identify a right triangle based on its angles. Correctly name the hypotenuse and the legs of a right triangle. Measure the sides of right triangles using decimal numbers. Compare two right triangles by looking at their hypotenuse and one leg. Understand that if two right triangles have the same hypotenuse and one leg length, they are 'the same size and shape'. Apply decimal division to solve problems involving side lengths of right triangles. Have you ever seen two triangles that look exactly alike? 🤔 What if we only knew the length of two special sides? Today, we'll explore special triangles called right triangles and learn about their unique parts: the hypotenuse and legs. We'll discover a cool way to tell if two right triangles ar...

TermDefinitionExample Right TriangleA triangle that has one angle that measures exactly 90 degrees (a square corner).A triangle with angles 90°, 45°, 45° is a right triangle. HypotenuseThe longest side of a right triangle, always found directly across from the 90-degree angle.In a right triangle with sides 3 cm, 4 cm, and 5 cm, the 5 cm side is the hypotenuse. LegsThe two shorter sides of a right triangle that meet to form the 90-degree angle.In a right triangle with sides 3 cm, 4 cm, and 5 cm, the 3 cm and 4 cm sides are the legs. Matching Triangles (Visual Congruence)Two triangles that have the exact same shape and size. If you could cut one out, it would fit perfectly on top of the other.Two identical slices of pizza, both cut from the same size pizza, are matching triangles. Decimal M...

Identifying the Hypotenuse In any right triangle, the hypotenuse is always the side that is opposite the right angle and is the longest side. Use this rule to correctly find the hypotenuse in any right triangle. Identifying the Legs In any right triangle, the two sides that form the right angle are called the legs. Use this rule to correctly find the two legs in any right triangle. The Hypotenuse-Leg Comparison Rule (Simplified) If you have two right triangles, and their hypotenuses are the same length, AND one of their legs is also the same length, then the two triangles are 'matching' (the same size and shape). This rule helps us quickly tell if two right triangles are identical without measuring all their sides or angles. It's a shortcut! Decima...