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

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  Transversal This is line that crosses two lines in a plane.

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.

Copying an angle Consider the angle below B 𝜄 O A To copy the angle above, we follow the following steps. Draw a line and label it CD as shown. 1. C D Position the compass at vertex of the angle and 2. draw an arc that intersects both rays as shown, B 𝜄 O A

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 C D 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

4. Join end O with the arc as shown. D C 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 of the arcs and the lines and draw intersecting arcs 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. If the line is not given you start by drawing a line 1. as shown. Position the compass needle on the line draw 2. arcs on both side of the compass. Label them A and B. B A

3. Using A as the center, draw arcs below and above the line as shown below. B A 4. Position the compass needle at B and draw arcs below and above the line as shown. B A

5. Join the intersections of the two pairs of arcs as shown. B A

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.

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 of the line segment.

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. A B C To do this, we follow the steps below Draw a line which passes through point C and 1. crosses line AB as shown.

. A B C 2. Position the compass at the intersection of line AB and the new line then draw an arc that crosses both lines as below. A B C

3. Using the compass width you used in step 2, position the compass at point C draw another arc shown below. A B C 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)

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. A B C 6. Join the intersection of the arcs and point C with a straight line. A B C

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.

A NSWERS TO HOMEWORK .

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