Model, including the use of drawing, concrete materials, and technology, the meaning, role, and use of the Pythagorean Theorem, using examples and non-examples.

Observe and analyze a set of triangles to judge if the Pythagorean Theorem could be used to determine an unknown side length and explain the reasoning.

Describe historical and contemporary applications of the Pythagorean Theorem, including the 3:4:5 ratio (e.g., Explain the relationship between a circle of string that has 13 equidistant knots or beads forming 12 spaces of equal length on it to the Pythagorean Theorem).

Relate, using examples, ratios equivalent to 3:4:5 and other Pythagorean Triples to the Pythagorean Theorem.

Develop, generalize, apply, and explain strategies to verify if a corner of a 3-D object is square (90°) or if a parallelogram is a rectangle.

Observe and analyze the lengths and intersections of diagonals of various quadrilaterals and draw conclusions.

Determine if given triangles are right triangles and explain the reasoning.

Create, solve, and verify the reasonableness of solutions to problems relevant to self, family, or community, for which the Pythagorean Theorem can be used.