Perpendicular Lines: Numbering in the drawing

Examples with solutions for Perpendicular Lines: Numbering in the drawing

Exercise #1

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

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

Our right angles are:

ABC,BCD,CDA,DAB ABC,BCD,CDA,DAB

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

Since in a rectangle we have 4 marked angles of 90 degrees, we must have 4 pairs of perpendicular lines.

Answer

4

Exercise #2

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

AAABBBCCCDDDEEEFFF

Video Solution

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,EFA,FAB ABC,BCD,CDE,DEF,EFA,FAB

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 EFA are: EF+FA

The lines that form angle FAB are: FA+AB

Since in the drawing we have 6 angles of 90 degrees marked, we must have 6 pairs of perpendicular lines.

Answer

6

Exercise #3

How many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

Let's draw straight lines extending from each of the four vertices of the shape to examine whether the angles are right angles.

The drawing will look like this:

AAABBBCCCDDD

From the drawing, we can see that angles DAB+CBA are greater than 90 degrees, while angles ADC+DCB are less than 90 degrees.

Since no right angles are marked in the drawing, there are 0 pairs of perpendicular lines in the drawing.

Answer

0

Exercise #4

How many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDDEEEFFFGGGHHH

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

We will draw straight lines coming from each of the marked points in the figure to examine whether the angles are right angles.

The drawing will look like this:

AAABBBCCCDDDEEEFFFGGGHHH

Note that the lines we drew create right angles, which are:

BAD,ABC,BCD,CDA,GEF,EGH,GHF,HFE BAD,ABC,BCD,CDA,GEF,EGH,GHF,HFE

The lines that form angle BAD are: BA+AD

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 GEF are: GE+EF

The lines that form angle EGH are: EG+GH

The lines that form angle GHF are: GH+HF

The lines that form angle HFE are: HF+FE

Since in the drawing we have 8 angles of 90 degrees marked, we must have 8 pairs of perpendicular lines.

Answer

8

Exercise #5

How many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

We will draw straight lines from each of the marked points in the figure to examine whether the angles are right angles.

The drawing will look like this:

AAABBBCCCDDD

Notice that from the drawing, angle BAD is greater than 90 degrees while angle CDA is less than 90 degrees.

The right angles in the drawing are:

ABC,DCB ABC,DCB

The lines that form angle ABC are: AB+BC

The lines that form angle DCB are: DC+CB

Notice that if we draw angle BAD and angle CDA, we can see that these angles are greater than 90 degrees, and therefore the lines that form them are not perpendicular.

Since there are 2 angles of 90 degrees marked in the drawing, we must have 2 pairs of perpendicular lines.

Answer

2

Exercise #6

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

AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLL

Video Solution

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

Exercise #7

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

AAABBBCCC

Video Solution

Step-by-Step Solution

Remember that perpendicular lines are vertical lines that form a right angle of 90 degrees between them.

The right angle we have in the drawing is: ABC

The lines that form the angle ABC are: AB+BC

Since we have one marked angle in the triangle, we must have a pair of perpendicular lines.

Answer

1

Exercise #8

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

AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines form a right angle of 90 degrees between them.

The right angles we have in the drawing are:

FAB,CDE FAB,CDE

The lines that create the angle FAB are: FA + AB

The lines that create the angle CDE are: CD + DE

Since we have 2 angles marked in the diagram, we therefore also have 2 pairs of perpendicular lines.

Answer

2

Exercise #9

How many pairs of perpendicular lines are there in the two squares shown below?

AAABBBCCCDDDEEEFFFGGGHHH

Video Solution

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,CDA,DAB,EFG,FGH,GHE,HEF ABC,BCD,CDA,DAB,EFG,FGH,GHE,HEF

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

Since we have 8 marked right angles of 90 degrees in the squares, we must have 8 pairs of perpendicular lines.

Answer

8

Exercise #10

How many vertices are shown in the figure?

CCCDDDEEEFFFAAABBBIIIJJJGGGHHH

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are straight lines that create a 90-degree angle at their intersection point.

Let's locate the intersection points that create right angles in the drawing:

CCCDDDEEEFFFAAABBBIIIJJJGGGHHH

The lines that create the marked right angles are:

AB is perpendicular to CD

AB is perpendicular to EF

EF is perpendicular to IJ

IJ is perpendicular to GH

Therefore, there are 4 perpendicular lines in the drawing.

Answer

5

Exercise #11

How many vertices are shown in the figure?

AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are straight lines that create a right angle of 90 degrees at their intersection point.

Let's locate the intersection points that create the right angles in the drawing.

The lines that create the right angles are:

AB is perpendicular to BC

BC is perpendicular to CD

CD is perpendicular to DA

DA is perpendicular to AB

BC is perpendicular to EF

AD is perpendicular to EF

Therefore, in the drawing there are 6 perpendicular lines.

Answer

6

Exercise #12

Determine how many pairs of perpendicular lines are shown in the diagram?

AAABBBCCCDDDEEE

Video Solution

Step-by-Step Solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

Our right angles are:

BAE,DEA BAE,DEA

The lines that form angle BAE are: BA+AE

The lines that form angle DEA are: DE+EA

Since in the drawing we have 2 angles of 90 degrees marked, we must have 2 pairs of perpendicular lines.

Answer

2

Exercise #13

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

Video Solution

Answer

12

Exercise #14

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

AAABBBCCCDDDEEEFFF

Video Solution

Answer

6

Exercise #15

Look at the diagram below and determine how many pairs of perpendicular lines there are.

AAABBBCCCDDDEEEFFF

Video Solution

Answer

2