Provide the student with basic instruction on the Pythagorean Theorem. Review the parts of a right triangle (e.g., vertices, right angle, acute angles, hypotenuse, and legs) and be sure the student understands the distinction between the legs and the hypotenuse. When initially introducing the Pythagorean Theorem, explicitly state the assumptions (a triangle is a right triangle with legs of lengths a and b and hypotenuse of length c) and the conclusion Describe the Pythagorean Theorem both verbally and in symbols and show applications of its use.
As needed, review the properties and theorems used in the proof: Angle-Angle Similarity Theorem, Distributive Property, Addition Property of Equality, Substitution Property and Cross Products Property of Proportions. Make clear what each property states and provide examples to demonstrate the application of each property.
Provide instruction on writing mathematical explanations, justifications, and proofs. Encourage the student to first consider the statement to be proven. Next, ask the student to examine the assumptions and then formulate an overall strategy. Make clear that every step must be justified with mathematical properties or theorems. Guide the student through the proof of the Pythagorean Theorem modeling the use of definitions, properties, or theorems to justify each step of the proof.
If necessary, review notation for naming sides (e.g., ) and describing lengths of sides (e.g., AD) and guide the student to use the notation appropriately.
Provide additional opportunities for the student to write informal proofs. Consider implementing MFAS tasks for standard 8.G.1.5 which ask the student to justify various angle relationships.