Difficulty: Hard

Average Score: 43%

Identify which of the following is a property of a right triangle.

Rationale

The hypotenuse is the side opposite from the right angle.

In a right triangle, the hypotenuse is specifically defined as the longest side, situated directly opposite the right angle. This characteristic is fundamental to the geometry of right triangles and is crucial for understanding their properties, especially in relation to the Pythagorean theorem.

A (The hypotenuse is the side opposite from the right angle) CORRECT

This statement accurately describes the definition of the hypotenuse in a right triangle. It is the longest side of the triangle, and its position opposite the right angle is a defining feature that distinguishes right triangles from other types.

B (The three angles add to 90 degrees) YOUR ANSWER

This statement is incorrect because, in any triangle, the sum of all three interior angles is always 180 degrees, not 90 degrees. A right triangle specifically contains one angle that measures 90 degrees, while the other two angles must together add up to 90 degrees to maintain the total of 180 degrees.

C (The triangle has three sides, which are all considered legs) YOUR ANSWER

This is misleading as, in a right triangle, there are specifically two legs (the sides that form the right angle) and one hypotenuse. The term "legs" refers only to the sides adjacent to the right angle, and thus the statement is inaccurate.

D (The hypotenuse equals the sum of the legs) YOUR ANSWER

This statement is incorrect because the relationship between the hypotenuse and the legs is defined by the Pythagorean theorem, which states that the square of the hypotenuse equals the sum of the squares of the legs, not the sum of their lengths.

Conclusion

In summary, the property of a right triangle that correctly identifies its defining feature is that the hypotenuse is the side opposite from the right angle. The incorrect choices either misrepresent fundamental triangle properties or confuse the relationships between the sides. Understanding these characteristics is essential for accurately applying geometric principles in various mathematical contexts.

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