Grade 8 - Shape and Space
Standard 8.SS.1 - Practice using Pythagorean Theorem to find the perimeter of a right triangle.
Included Skills: Geometry
Demonstrate understanding of the Pythagorean Theorem concretely or pictorially and symbolically and by solving problems. • Generalize the results of an investigation of the expression a² + b²= c² (where a, b, and c are the lengths of the sides of a right triangle, c being the longest): - concretely (by cutting up areas represented by a² and b² and fitting the two areas onto c²) - pictorially (by using technology) - symbolically (by confirming that a² + b² = c² for a right triangle). • Explore right and non-right triangles, using technology, and generalize the relationship between the type of triangle and the Pythagorean Theorem (i.e., if the sides of a triangle satisfy the Pythagorean equation, then the triangle is a right triangle which is known as the Converse of the Pythagorean Theorem). • Explore right triangles, using technology, using the Pythagorean Theorem to identify Pythagorean triples (e.g., 3, 4, 5 or 5, 12, 13), hypothesize about the nature of triangles with side lengths that are multiples of the Pythagorean triples, and verify the hypothesis. • Create and solve problems involving the Pythagorean Theorem, Pythagorean triples, or the Converse of the Pythagorean Theorem. • Give a presentation that explains a historical or personal use or story of the Pythagorean Theorem (e.g., Pythagoras and his denial of irrational numbers, the use of the 3:4:5 right triangle ratio in the Pyramids, squaring off the corner of a sandbox being built for a sibling, or determining the straight line distance between two towns to be travelled on a snowmobile).