Final answer:
The statement that FGH is a right angle triangle with the given measurements is True. This is verified by the Pythagorean theorem, which confirms that the sum of the squares of the legs equals the square of the hypotenuse.
Step-by-step explanation:
The statement that FGH is a right angle triangle with hypotenuse 9, the right leg √45, and the bottom leg 6 needs to be verified using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
To verify the statement, we calculate:
- Right leg (√45) squared is: (√45)² = 45
- Bottom leg (6) squared is: 6² = 36
- Sum of the squares of the legs: 45 + 36 = 81
- The square of the hypotenuse (9) is: 9² = 81
Since the sum of the squares of the legs is equal to the square of the hypotenuse, the statement conforms to the Pythagorean theorem; therefore, the statement is True.