Question

what is the pythagorean theorem?
a. a + b = c
b. a² + b² = c²
c. a² - b² = c²
d. a × b = c
according to the pythagorean theorems converse, if a = 5, b = 12, and c = 13, what type of triangle is it?
a. right triangle
b. obtuse triangle
c. acute triangle
d. equilateral triangle

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle with legs of lengths $a$ and $b$ and hypotenuse of length $c$ is $a^{2}+b^{2}=c^{2}$.

Step2: Apply converse of Pythagorean theorem

For $a = 5$, $b = 12$, and $c = 13$, calculate $a^{2}+b^{2}$ and $c^{2}$.
$a^{2}=5^{2}=25$, $b^{2}=12^{2}=144$, so $a^{2}+b^{2}=25 + 144=169$. And $c^{2}=13^{2}=169$. Since $a^{2}+b^{2}=c^{2}$, by the converse of the Pythagorean theorem, the triangle is a right - triangle.

Answer:

1. b. $a^{2}+b^{2}=c^{2}$
2. a. Right triangle