Question

1. which of the following statements is not a true statement?

a. the legs of a triangle are the sides adjacent to the right angle.
b. the hypotenuse is directly across from the right angle.
c. the pythagorean theorem can only be used with right triangles.
d. the hypotenuse is always the shortest side length.

Explanation:

• Option A: In a right triangle, the two sides forming the right angle are defined as legs, so this is true.
• Option B: The hypotenuse is specifically the side opposite the right angle in a right triangle, so this is true.
• Option C: The Pythagorean theorem ($a^2 + b^2 = c^2$) relies on the presence of a right angle to hold, so it only applies to right triangles, making this true.
• Option D: The hypotenuse is opposite the largest angle (90 degrees) in a right triangle, so it must be the longest side, not the shortest. This statement is false.

Answer:

D. The hypotenuse is always the shortest side length.