Evidence of Understanding

**use triangle similarity and scale factor to prove relationships for right triangles**- prove the
**Pythagorean Theorem (**__proof of the Pythagorean theorem using similarity__) - use similarity to analyze relationships between the altitude and the lengths of the two segments of the hypotenuse
- prove the length of the altitude drawn from the vertex of the right angle is the
**geometric mean**between the lengths of the two segments of the hypotenuse (__video)__ - calculate the length of an altitude or one of the two segments of the hypotenuse

- prove the length of the altitude drawn from the vertex of the right angle is the

- prove the
**analyze characteristics of triangles using the Pythagorean Theorem**- classify a triangle as acute, right, or obtuse using the Pythagorean theorem
- use an
__area model__to explain that when a^{2}+ b^{2}> c^{2}, the triangle is acute; that when a^{2}+ b^{2}= c^{2}, the triangle is right; and that when a^{2}+ b^{2 }< c^{2}, the triangle is obtuse

- use an
- analyze and describe special
**Pythagorean triples**using similarity and scale factor- explain that special triples occur when a
^{2}+ b^{2}is a**perfect square**and use this to strategically name Pythagorean triples - use similarity to explain and name other triangles that are similar to the 3-4-5, 5-12-13, 8-15-17, or other Pythagorean triples

- explain that special triples occur when a

- classify a triangle as acute, right, or obtuse using the Pythagorean theorem
**find the missing side length of a right triangle using Pythagorean Theorem**- create diagrams to model situations and use Pythagorean Theorem to solve them
- use right triangles and their properties to describe objects and/or situations
- use properties of similar triangles and scale factor with the Pythagorean Theorem

- use a Pythagorean triple, when applicable, to state missing side lengths

- create diagrams to model situations and use Pythagorean Theorem to solve them

Develop conceptual understanding:

Pythagorean Theorem, geometric mean, acute triangle, obtuse triangle, right triangle, perfect square, Pythagorean tripleSupporting terms to communicate:

perpendicular, altitude, vertex, corresponding, leg, hypotenuse, right angle, acute angle, obtuse angle, similar, scale factor, proportional, ratio