Unit 3, Lesson 14
Proving the Pythagorean Theorem
Geometry
Practice
Problem 2
In right triangle \(ABC\), a square is drawn on each of its sides. An altitude \(CD\) is drawn to the hypotenuse \(AB\) and extended to the opposite side of the square on \(FE\). In class, we discussed Elena’s observation that \(a^2=xc\) and Diego’s observation that \(b^2=yc\). Mai observes that these statements can be thought of as claims about the areas of rectangles.
- Which rectangle has the same area as \(BGHC\)?
- Which rectangle has the same area as \(ACIJ\)?
Right triangle A B C with sides a, b and c = x + y. Squares are on each side. A C I J is on b, B C H G is on a and A B E F is on c. An altitude C D labeled h is drawn to the hypotenuse A B and extended to the opposite side of the square on F E at K. A D is labeled y, the smaller D B is x and B E is c = x + y.