Question

if (a^{2}+b^{2}>c^{2}), what type of triangle is formed?
a. isosceles triangle
b. scalene triangle
c. right triangle
d. acute triangle
which statement correctly defines the converse of the pythagorean theorem?
a. if a triangle is a right triangle, then (a^{2}+b^{2}=c^{2}).
b. if (a^{2}+b^{2}>c^{2}), then the triangle is a right triangle.
c. if (a^{2}+b^{2}<c^{2}), then the triangle is a right triangle.

Explanation:

Step1: Recall triangle - inequality rules

For a triangle with side lengths $a$, $b$, and $c$ (where $c$ is the longest side), if $a^{2}+b^{2}>c^{2}$, the triangle is acute. If $a^{2}+b^{2}=c^{2}$, it is a right - triangle. If $a^{2}+b^{2}

Step2: Recall the converse of the Pythagorean Theorem

The converse of the Pythagorean Theorem states that if a triangle has side lengths $a$, $b$, and $c$ such that $a^{2}+b^{2}=c^{2}$, then the triangle is a right triangle. In other words, if a triangle is a right triangle, then $a^{2}+b^{2}=c^{2}$, which is option a for the second question.

Answer:

1. d. Acute triangle
2. a. If a triangle is a right triangle, then $a^{2}+b^{2}=c^{2}$.