Left Panel Interactive

Statements

Reasons

1. c is the longest side in △ABC, a² + b² > c²

1. given

2. Draw △DEF with right ∠F, legs a and b, and hypotenuse n

2. def. of right triangle

3. a² + b² = n²

3. Pythagorean theorem

4. n² > c²

4. substitution property

5. n > c

5. square root property of equality

6. m∠F > m∠C

6. converse hinge theorem

7. m∠F = 90°

7. def. of right angle

8. 90° > m∠C

8. substitution property

9. ∠C is an acute angle

9. def. of acute angle

10. C is the largest angle in △ABC

10. triangle parts theorem

11. △ABC is an acute triangle

11. def. of acute triangle