Geometry

Question Analysis

The main focus is to use the Pythagorean Theorem Converse to determine if the corners of the picture frame are right - angled. We need to check if the sum of the squares of the two adjacent sides of the frame (the legs of a potential right - triangle) equals the square of the diagonal of the frame (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 picture frame, if the triangle formed by two adjacent sides and the diagonal is a right - triangle, the frame has right - angled corners.

Step - by - Step Solution

1. Identify the sides:

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

2. Calculate the squares:

, , and .

3. Check the relationship:

Calculate :

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