Questions answered
The diagram shows a larger square divided into a smaller square and four right triangles. The
diagram can be used to prove the Pythagorean theorem.
18
Time
elapsed
рь
a
00
23
13
HR MIN SEC
a
bd
a
SmartScore
out of 100
Complete the proof of the Pythagorean theorem.
76
9
The area of the larger square found by multiplying its side lengths is
The smaller
square has side lengths of a - b. The combined area of the four triangles and the smaller
square is
which is equivalent to a? - 2ab + b² + 2ab. a? - 2ab +
b2 + 2ab is also equivalent to
. This expression and the expression found by
multiplying the larger square's side lengths both represent the same area. Therefore,