Question

1. choose the correct answer.

the side opposite the right angle in a right triangle is called the

hypotenuse

adjacent side

leg

nonincluded side

1. choose the correct answer.

the equation for the pythagorean theorem is

a = a

if a = b and b = c, then a = c.

if a = b then b = a.

c² = a² + b²

Explanation:

1. In a right - triangle, by definition, the side opposite the right angle is called the hypotenuse. The adjacent side is relative to an acute angle (not the right angle). A leg is one of the two sides forming the right angle. A non - included side is a term more relevant in triangle congruence (e.g., in AAS - Angle - Angle - Side congruence) and not the standard term for the side opposite the right angle.
2. The Pythagorean Theorem states that in a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), the relationship between the sides is \(c^{2}=a^{2}+b^{2}\). The equation \(a = a\) is the reflexive property of equality. The statement “If \(a = b\) and \(b = c\), then \(a = c\)” is the transitive property of equality. The statement “If \(a = b\) then \(b = a\)” is the symmetric property of equality.

Answer:

1. hypotenuse
2. \(c^{2}=a^{2}+b^{2}\)