Finding Perpendicular Line Pairs: Cross-Shaped Geometric Analysis

Question

How many pairs of perpendicular lines are there in the diagram below?

AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLL

Video Solution

Solution Steps

00:00 How many perpendiculars are there in the drawing?
00:04 A perpendicular creates a right angle at the intersection point between the lines
00:08 Let's mark and count all the right angles
00:28 And this is the solution to the question

Step-by-Step Solution

Let's remember that perpendicular lines are lines that intersect at a right angle of 90 degrees.

Our right angles are:

ABC,BCD,CDE,DEF,EFG,FGH,GHI,HIJ,IJK,JKL,KLA,LAB ABC,BCD,CDE,DEF,EFG,FGH,GHI,HIJ,IJK,JKL,KLA,LAB

The lines that form angle ABC are: AB+BC

The lines that form angle BCD are: BC+CD

The lines that form angle CDE are: CD+DE

The lines that form angle DEF are: DE+EF

The lines that form angle EFG are: EF+FG

The lines that form angle FGH are: FG+GH

The lines that form angle GHI are: GH+HI

The lines that form angle HIJ are: HI+IJ

The lines that form angle IJK are: IJ+JK

The lines that form angle JKL are: JK+KL

The lines that form angle KLA are: KL+LA

The lines that form angle LAB are: LA+AB

Since in the drawing we have 12 angles of 90 degrees marked, we must have 12 pairs of perpendicular lines.

Answer

12