Ohio Resource Center
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Lessons
Pythagorean Puzzle
Discipline
Mathematics
Grades
7, 8
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Professional Commentary

In this self-guided investigation, students use Geometer’s Sketchpad ® to construct a right triangle and discover a geometric proof of the Pythagorean Theorem. Students test the geometric proof with acute and obtuse triangles. Activity sheets and scoring guides for the teacher are included. (author/sw)


Common Core State Standards for Mathematics
Grade 7
Geometry
Draw, construct, and describe geometrical figures and describe the relationships between them.
7.G.A.1 
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.A.2 
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.6 
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.
Grade 8
Geometry
Understand and apply the Pythagorean Theorem.
8.G.B.6 
Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7 
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (8–10)
E.
Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.
H.
Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
Grade Level Indicators (Grade 10)
3.
Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including: a. prove the Pythagorean Theorem; b. prove theorems involving triangle similarity and congruence; c. prove theorems involving properties of lines, angles, triangles and quadrilaterals; and d. test a conjecture using basic constructions made with a compass and straightedge or technology.
4.
Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software.
Principles and Standards for School Mathematics
Geometry Standard
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Expectations (9–12)
establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (9–12)
establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;
draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;