Question

exam 7
question 1: standard g.srt.8
how many ways are there to prove the pythagorean theorem?
a. 2
b. 1
c. over 100
d. over 350

question 2: standard g.srt.8
which type of triangles does the pythagorean theorem work in?
a. isosceles
b. equilateral
c. all types of triangles
d. right

question 3: standard g.srt.8
which side of the triangle has to be labeled \c\?
a. leg
b. hypotenuse
c. opposite
d. adjacent

question 4: standard g.srt.8
john labeled his triangle so he can use the pythagorean theorem. what is wrong with his labeling?
image of a right triangle with legs labeled a and c, hypotenuse labeled b
a. the hypotenuse is mislabeled as \b\
b. the legs should be switched
c. there is nothing wrong, he labeled it correctly
d. the hypotenuse is mislabeled as \a\

Explanation:

Question 1

The Pythagorean theorem has been proven in over 350 different ways, including geometric, algebraic, and other methods.

The Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\)) applies specifically to right - angled triangles, where \(c\) is the hypotenuse (the side opposite the right angle) and \(a\) and \(b\) are the legs (the other two sides). Isosceles triangles don't necessarily have a right angle, equilateral triangles have all angles equal to \(60^{\circ}\) (not right - angled), and the theorem does not work for all types of triangles, only right - angled ones.

In the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), the side labeled \(c\) is the hypotenuse. The hypotenuse is the side opposite the right angle in a right - angled triangle and is the longest side. Legs are the other two sides (labeled \(a\) and \(b\) usually), and "opposite" and "adjacent" are terms related to angles in trigonometry but \(c\) is defined as the hypotenuse.

Answer:

d. Over 350

Question 2