Math Games

Grade 8 - Shape and Space

Standard 8.SS.1 - Practice using Pythagorean Theorem to find the hypotenuse of a right triangle.

Included Skills:

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).