Complete the proof of the Pythagorean theorem. Given: △ is a right triangle, with
a right angle at ∠.
Prove: ^2
+^2
= ^2

Statement Reason
1. △ is a right triangle, with a right angle
at ∠.
1. Given
2. Draw an altitude from point C to. 2. From a point not on a line, exactly one
perpendicular can be drawn through the point to
the line.
3. ∠ and ∠ are right angles. 3. Definition of altitude
4. ∠ ≅ ∠ 4. All right angles are congruent.
5. ∠ ≅ ∠ 5.
6. 6. AA Similarity Postulate
7.
/x
=
/a
7.
8. ^2= 8.
9. ∠ ≅ ∠ 9.
10. ∠ ≅ ∠ 10.
11. 11. AA Similarity Postulate
Statement Reason
12. /y
=c/b
= 12.
13. ^2 = 13.
14. ^2+ ^2 = + 14.
15. 15. Distributive Property
16. + = 16.
17. ^2+b^2=c^2 17.