Copying a line segment To copy a line segment, draw a line similar - - PowerPoint PPT Presentation

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D AY 39 S UMMARY OF BASIC GEOMETRIC CONSTRUCTION I NTRODUCTION We have discussed different methods and tools used in geometric construction in previous lessons. We are going to summarize those methods in this lesson. V OCABULARY

SLIDE 1

DAY 39 – SUMMARY OF BASIC

GEOMETRIC CONSTRUCTION

SLIDE 2

INTRODUCTION

We have discussed different methods and tools used in geometric construction in previous lessons. We are going to summarize those methods in this lesson.

SLIDE 3

VOCABULARY

 Transversal

This is line that crosses two lines in a plane.

SLIDE 4

Copying a line segment To copy a line segment, draw a line similar but longer than the line that you want to copy then position the compass needle at one end of the line that you are copying and extend it to the other end. Next, position the compass needle at one end of the line you drew and without changing the radius of the compass, make an arc on the line. The section of the line from that end to the arc is similar to the original line.

SLIDE 5

Copying an angle Consider the angle below To copy the angle above, we follow the following steps.

1.

Draw a line and label it CD as shown.

2.

Position the compass at vertex of the angle and draw an arc that intersects both rays as shown,

𝜄 A O B 𝜄 A O B C D

SLIDE 6

3. Using the same compass radius position the

compass at C and make an arc that intersects line CD as shown. Label the arc as Q

4. Use the compass to measure the distance between

the intersections of the arc you drew in step 2.

5. Using this distance position the compass at the

intersection of the arc Q and line CD and draw an arc that intersects Q as shown below.

C D Q C D Q

SLIDE 7

4. Join end O with the arc as shown.

C D Q

SLIDE 8

Bisecting an angle To bisect an angle, first you position the compass needle at the vertex of the angle you are bisecting and make arcs on each adjacent side as shown below. Next, position the compass at the points of intersection

f the arcs and the lines and draw intersecting arcs

with a radius which is greater than the one you used previously as shown below.

SLIDE 9

The next step is to join the vertex with the intersection of the two arcs as shown below. This line divides the angle into two equal angles which are congruent.

SLIDE 10

Constructing perpendicular lines The following steps are followed to construct perpendicular lines.

1.

If the line is not given you start by drawing a line as shown.

2.

Position the compass needle on the line draw arcs on both side of the compass. Label them A and B.

A B

SLIDE 11

3. Using A as the center, draw arcs below and

above the line as shown below.

4. Position the compass needle at B and draw arcs

below and above the line as shown.

A B A B

SLIDE 12

5. Join the intersections of the two pairs of arcs as

shown.

A B

SLIDE 13

Constructing the perpendicular bisector of a line segment

1. To Construct a perpendicular bisector of a line

segment, the following steps are followed.

2. Position the compass at one end of the line segment

and stretch it more than half of the line segment. Make arcs above and below the line segment as shown.

SLIDE 14

3. Position the compass on the other end of the line

segment and draw arcs below and above the line segment.

4. Join the intersections of the arcs with a straight

line. The resulting line is the perpendicular bisector of the line segment and passes through the midpoint

f the line segment.

SLIDE 15

Constructing parallel lines We are going to discuss how we can construct a line parallel to a given line through a point not in the line. In the diagram below, a line parallel to line AB through point C can be constructed. To do this, we follow the steps below

1.

Draw a line which passes through point C and crosses line AB as shown.

C A B

SLIDE 16

.

2. Position the compass at the intersection of line

AB and the new line then draw an arc that crosses both lines as below.

C A B C A B

SLIDE 17

3. Using the compass width you used in step 2,

position the compass at point C draw another arc shown below.

4. Position the compass at where the first arc

intersects the transverse line and extend it to where the same arc intersects line AB.(we want to copy the angle that the transversal makes with line AB)

C A B

SLIDE 18

5. Move the compass to the intersection of the

second arc and transverse line then draw an arc that intersects the second arc as shown.

6. Join the intersection of the arcs and point C with

a straight line.

C A B C A B

SLIDE 19

Example Construct a line passing through point P and parallel to line MN.

N

SLIDE 20

Solution

N

SLIDE 21

HOMEWORK Construct a perpendicular bisector to the line segment given below.

SLIDE 22

ANSWERS TO HOMEWORK

.

SLIDE 23

DAY 39 – SUMMARY OF BASIC

GEOMETRIC CONSTRUCTION

INTRODUCTION

We have discussed different methods and tools used in geometric construction in previous lessons. We are going to summarize those methods in this lesson.

VOCABULARY

 Transversal

This is line that crosses two lines in a plane.

Copying an angle Consider the angle below To copy the angle above, we follow the following steps.

1.

Draw a line and label it CD as shown.

2.

Position the compass at vertex of the angle and draw an arc that intersects both rays as shown,

𝜄 A O B 𝜄 A O B C D

compass at C and make an arc that intersects line CD as shown. Label the arc as Q

the intersections of the arc you drew in step 2.

intersection of the arc Q and line CD and draw an arc that intersects Q as shown below.

C D Q C D Q

C D Q

Bisecting an angle To bisect an angle, first you position the compass needle at the vertex of the angle you are bisecting and make arcs on each adjacent side as shown below. Next, position the compass at the points of intersection

with a radius which is greater than the one you used previously as shown below.

The next step is to join the vertex with the intersection of the two arcs as shown below. This line divides the angle into two equal angles which are congruent.

Constructing perpendicular lines The following steps are followed to construct perpendicular lines.

1.

If the line is not given you start by drawing a line as shown.

2.

Position the compass needle on the line draw arcs on both side of the compass. Label them A and B.

A B

above the line as shown below.

below and above the line as shown.

A B A B

shown.

A B

Constructing the perpendicular bisector of a line segment

segment, the following steps are followed.

and stretch it more than half of the line segment. Make arcs above and below the line segment as shown.

segment and draw arcs below and above the line segment.

line. The resulting line is the perpendicular bisector of the line segment and passes through the midpoint

Constructing parallel lines We are going to discuss how we can construct a line parallel to a given line through a point not in the line. In the diagram below, a line parallel to line AB through point C can be constructed. To do this, we follow the steps below

1.

Draw a line which passes through point C and crosses line AB as shown.

C A B

.

AB and the new line then draw an arc that crosses both lines as below.

C A B C A B

position the compass at point C draw another arc shown below.

intersects the transverse line and extend it to where the same arc intersects line AB.(we want to copy the angle that the transversal makes with line AB)

C A B

second arc and transverse line then draw an arc that intersects the second arc as shown.

a straight line.

C A B C A B

Example Construct a line passing through point P and parallel to line MN.

N

Solution

N

HOMEWORK Construct a perpendicular bisector to the line segment given below.

ANSWERS TO HOMEWORK

.

THE END