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1
In a right-angled triangle, what is the fundamental relationship defined by the Pythagorean theorem?
A
The sum of the two shorter sides equals the longest side.
B
The product of the two shorter sides equals the square of the hypotenuse.
C
The square of the hypotenuse is equal to the sum of the squares of the other two sides.
D
The hypotenuse is always equal to the sum of the other two sides.
2
If a right triangle has legs measuring 3 cm and 4 cm, what is the length of the hypotenuse?
A
5 cm
B
25 cm
C
12 cm
D
7 cm
3
Which of the following sets of side lengths represents a valid right-angled triangle?
A
6 cm, 8 cm, 12 cm
B
2 cm, 3 cm, 4 cm
C
1 cm, 1 cm, 2 cm
D
5 cm, 12 cm, 13 cm
4
How can the Pythagorean theorem be used to determine if a triangle is NOT a right triangle?
A
By confirming that all three sides are of equal length.
B
By checking if the sum of all angles is 180 degrees.
C
By measuring the perimeter of the triangle.
D
By verifying if the square of the longest side is unequal to the sum of the squares of the other two sides.
5
In the triangle formula a^2 + b^2 = c^2, what specific condition must be met for the formula to be applicable?
A
The triangle must have all sides of different lengths.
B
The triangle must contain exactly one 90-degree angle.
C
The triangle must be an equilateral triangle.
D
The triangle must have at least one obtuse angle.