Applying The Pythagorean Theorem P3

Cluster: Understand And Apply The Pythagorean Theorem 3

Task Overview: This lesson builds upon Pt2 of The Pythagorean Theorem. Within the lesson, students will make connections to real-world application problems that deal with drawing right triangles to find the missing sides. Students will use these connections to prove why their triangles are labeled the way they are as they make sense of the math in each scenario. This lesson is designed with heavy application of the conceptual understanding of the theorem.

8.G.B.7 Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.

This standard focuses on the application of the Pythagorean Theorem. Students will apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in both two and three-dimensional objects.

8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

This standard uses the Pythagorean Theorem as an application to find the distance between two non-vertical and non-horizontal points on a line. Given two points, students are able to draw a line connecting the points and create a right triangle using the points.

Objectives

Students should be able to successful identify the sides of a right triangle from real-world problems and effectively compute the length of the missing leg or hypotenuse
Students should be able to create right angles from non-vertical and non-horizontal line segments and use it to compute the hypotenuse.

Prerequisites

• 8.G.B.6 & 8.G.B.7 – Explain a proof of the Pythagorean Theorem and its converse.
• Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (7.G.B.6)
• Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. (8.EE.A.2)