Determine whether the statement is always true, sometimes true, or never true.
3) The length of the hypotenuse of a right triangle equals the length of one of the legs of the triangle.
Answer choice: a.) always true b.) sometimes true c.)never true
Think about this in terms of the a^2+b^2=c^2. Could a or b possibly be the same length as c?
PJ is citing the Pythagorean theorem.
(side a)^2 + (side b)^2 = hypotenuse^2
What would have to happen for either side = hypotenuse?
you.
Determine if the following is always, sometimes, or never true.
y = -1/5 x + 3 is a function.
A Always
B Sometimes
C Never
always true
To determine whether the statement is always true, sometimes true, or never true, we need to analyze the properties of a right triangle.
In a right triangle, the hypotenuse is always the side opposite the right angle. By the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, mathematically, we have:
c^2 = a^2 + b^2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
Considering this equation, we can conclude that the length of the hypotenuse is always different from the lengths of the other two sides unless one of the legs has a length of zero. In that case, the hypotenuse would also have a length of zero, resulting in it being equal to one of the legs.
Therefore, the statement "The length of the hypotenuse of a right triangle equals the length of one of the legs of the triangle" is only true when one of the legs has a length of zero, which makes it sometimes true.
So, the correct answer choice is b.) sometimes true.