Determine how many pairs of perpendicular lines are there in the two squares shown below:
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Determine how many pairs of perpendicular lines are there in the two squares shown below:
Remember that perpendicular lines are lines that intersect at a right angle of 90 degrees.
Our right angles are:
The lines that form angle ABC are: AB+BC
The lines that form angle BCD are: BC+CD
The lines that form angle CDA are: CD+DA
The lines that form angle DAB are: DA+AB
The lines that form angle EFG are: EF+FG
The lines that form angle FGH are: FG+GH
The lines that form angle GHE are: GH+HE
The lines that form angle HEF are: HE+EF
Given that we have 8 marked right angles of 90 degrees in the squares, we must have 8 pairs of perpendicular lines.
8
What do the four figures have in common?
A perpendicular pair is two lines that meet at a 90° angle. In the diagram, lines AB and BC form one pair because they meet at corner B with a right angle symbol.
Diagonals in squares meet at 45° angles, not 90°. Only adjacent sides of squares are perpendicular to each other, which is why we see right angle symbols at the corners.
No! Each corner represents one perpendicular pair, regardless of which square it belongs to. Corner intersections are shared, not doubled.
Look for the small square symbols at each corner - these mark right angles. Count them: 4 in the outer square + 4 in the inner square = 8 perpendicular pairs total.
The number of perpendicular pairs would remain the same! Each square always has 4 corners with right angles, so two squares always give 8 perpendicular pairs regardless of orientation.
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