Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to determine whether the corners of the coaster are right-angled. We need to check if the sum of the squares of the two adjacent sides of the coaster (which would act as the legs of a right triangle) is equal to the square of the diagonal of the coaster (the hypotenuse of the right triangle).

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. In the case of the coaster, if the triangle formed by the two adjacent sides and the diagonal satisfies this equation, the coaster has right-angled corners.

Step - by - Step Solution

1. Identify the sides:

Let cm and cm be the adjacent sides of the coaster, and cm be the diagonal.

2. Calculate the squares:

, , and .

3. Check the relationship:

Calculate

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