Square Geometry: Analyzing Perpendicular Diagonals in a Given Square

Let's remember that perpendicular lines are lines that intersect at a 90-degree angle.

According to the properties of the square, all angles measure 90 degrees and the diagonals are bisectors.

We will focus on the upper triangle formed by the diagonals intersecting each other.

Since all angles measure 90 degrees, the diagonals form two 45-degree angles.

We will draw this as follows:

Calculate the missing third angle in the triangle, marked with a question mark, as follows.

The sum of the angles of a triangle equals 180 degrees, so the formula to find the third angle is:

$180-45-45=$

$180-45=135$

$135-45=90$

Since the third angle equals 90 degrees, its complementary angle also equals 90 degrees:

Since the diagonals form a 90-degree angle between them, they are indeed perpendicular and perpendicular to each other.