Question

which best describes the application of the pythagorean theorem converse?
a to determine if a shape is a triangle
b to determine if a triangle is a right triangle.
c to determine a missing side length of a triangle
d to determine the missing side length of a right triangle.
by the converse of the pythagorean theorem, which best identifies if a triangle is an acute triar
a if ( c^{2}>a^{2}+b^{2} ), then the triangle is acute.
b if ( c^{2}=a^{2}+b^{2} ), then the triangle is acute.
c if ( c
eq a^{2}+b^{2} ), then the triangle is acute.
d if ( c^{2}<a^{2}+b^{2} ), then the triangle is acute.

Explanation:

First Question:

Step1: Analyze each option for the first question

• Option A: The Pythagorean theorem converse is not used to determine if a shape is a triangle. A shape with three sides is a triangle by definition.
• Option B: The converse of the Pythagorean theorem states that if \(a^{2}+b^{2}=c^{2}\) (where \(a\), \(b\) are the lengths of two sides and \(c\) is the length of the longest side of a triangle), then the triangle is a right - triangle. This is the correct application.
• Option C: The Pythagorean theorem (not its converse) is used to find a missing side length of a right - triangle. The converse is about determining the type of triangle.
• Option D: Again, this is the use of the Pythagorean theorem (not its converse) for a right - triangle.

Second Question:

Step1: Recall the rules for classifying triangles using the Pythagorean theorem and its extensions

Let \(a\), \(b\) be the lengths of two sides and \(c\) be the length of the longest side of a triangle.

• If \(c^{2}=a^{2}+b^{2}\), the triangle is a right - triangle (by the Pythagorean theorem converse).
• If \(c^{2}
• If \(c^{2}>a^{2}+b^{2}\), the triangle is obtuse.

Answer:

1. B. To determine if a triangle is a right triangle.
2. D. If \(c^{2}