Constructing perpendicular lines with a compass and a straightedge. - - PowerPoint PPT Presentation

DAY 37 – CONSTRUCTING

PERPENDICULAR LINES

INTRODUCTION

Two lines which intersect making a right angle are said to be perpendicular. In this lesson, we are going to learn various methods that we can use to construct lines intersecting at the right angle.

VOCABULARY

 Line segment

This is a section of a line between two points. Perpendicular lines Are two lines which intersect making a right angle

Constructing perpendicular lines with a compass and a straightedge. Given a horizontal line AB, we can draw a line perpendicular to it at point P by following the steps below. Position the needle of the compass at P then draw the arcs of the same radius to intersect the line on both sides

• f P.

C D P A B

• 2. Draw two arcs; one below the line and another one

above the line as shown below using C as the center.

C D P A B

• 3. Position the compass needle at D and without

changing its radius, draw arcs below and above the line as shown below.

C D P A B

• 4. Join the intersections of the two pairs of arcs

with a straight line as shown below. This results to a vertical line which is perpendicular to AB. The same method can also be used to draw a perpendicular bisector where A and D are taken to be the end points of the line to be bisected.

C D P A B

Still using the compass, we can construct perpendicular line using the following the steps

• 1. Draw a line segment.
• 2. Identify any point on the line segment and label it O.
• 3. Position the needle of the compass at O and draw a

semi-circle centered at the midpoint and with its circumference passing through the endpoints of the line as shown.

O

• 4. Without changing the radius of the compass,

position the needle of the compass on one end and draw an arc that intersects the semi-circle. Label it as A.

• 5. Using the same compass radius, position the

compass needle on the other end of the semicircle and draw an arc that intersects the semi-circle. Label it B.

• 6. Using the same compass radius, position the

compass needle at A and draw an arc above it.

• 7. Using the same compass radius, position the

compass needle at B and draw an above B.

O A B

. Join the point O with the two intersecting arcs as shown below. This results to a line which is perpendicular to AB.

O A B O A B

Constructing a perpendicular line through a given point. Sometimes we might be required to construct a perpendicular line to given line segment through a given point. For instance, we may be required to construct a line perpendicular to line AB through point P. To this, we follow the steps below.

• 1. Position the needle of the compass at P then

draw the arcs of the same radius to intersect the line on both sides of P. Label them C and D respectively.

A B P

2.Position the compass needle at C and draw an arc above AB as shown.

• 3. Position the compass needle at D and without

changing its radius, draw an arc above line AB as shown below.

A B P C D A B P C D

• 3. Position the compass needle at D and without

changing its radius, draw an arc above line AB as shown below.

• 4. Join the intersection of the two arcs with point P.

The resulting line is perpendicular to AB and passes through point P.

A B P C D A B P C D

Constructing perpendicular lines with a string. A string can also be used to construct perpendicular

• lines. To do this, a string is tied to the pencil, and the
• ther end of the string positioned on one endpoint of

the line given. For accuracy, we can use a push pin to position the string. We then draw a circle around the endpoint with a center at that endpoint as shown below. Next, we move the string to the other endpoint and draw a circle around that endpoint as shown.

. We then draw a straight line which passes through the intersections of the two circles as shown in the next slide.

. This results to a new line which is perpendicular to the original line.

Constructing perpendicular lines with a reflective device e.g., plane mirror To do this, we follow the following steps.

• 1. Draw the line segment
• 2. Place the mirror vertically and crossing the line

segment.

• 3. Adjust the mirror until the reflection of the line

segment appears as a continuation of the line segment.

• 4. Hold the mirror in that position and then draw a

straight line using the mirror as the straight edge. The resulting line is perpendicular to the line segment.

Constructing perpendicular lines by paper folding We first draw a line segment on a translucent paper then we fold the paper across the line segment such the endpoints of the line segment

• coincide. This folding creates a crease across the

line segment. Draw a line along the crease created. This results in a perpendicular line passing through the midpoint of the original line segment.

Example Draw an horizontal line of length 2 in and construct a line perpendicular to it using a string and a straightedge. Solution

HOMEWORK Using a compass and a straightedge construct a line which is perpendicular to the line given below.

ANSWERS TO HOMEWORK

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THE END