Geometry

Question Analysis

The main focus is to apply the Pythagorean Theorem Converse to figure out if the given triangle is a right - triangle. We need to check if the sum of the squares of the two shorter sides equals the square of the longest side.

 

Key Concept Explanation

The Pythagorean Theorem Converse states that for a triangle with side lengths , , and  (where  is the longest side), if , then the triangle is a right - triangle.

 

Step - by - Step Solution

1. Identify the longest side:

 Calculate the squares of the sides: , , .

 By comparing, the longest side , and the two shorter sides are  and .

2. Calculate the sum of the squares of the two shorter sides:

 

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