Download Copying Segments and Angles - 3-D Math DR. D. Dambreville`s

Copying Segments and Angles
Adapted from Walch Education
Key Concepts
• A geometric figure precisely created using only a
straightedge and compass is called a construction.
• A straightedge can be used with patty paper (tracing
paper) or a reflecting device to create precise
representations.
• Constructions are different from drawings or sketches.
• A drawing is a precise representation of a figure,
created with measurement tools such as a protractor
and a ruler.
1.2.1: Copying Segments and Angles
2
Concepts, continued
• A sketch is a quickly done representation of a figure or
a rough approximation of a figure.
• When constructing figures, it is very important not to
erase your markings.
• Markings show that your figure was constructed and
not measured and drawn.
• An endpoint is either of two points that mark the ends
of a line, or the point that marks the end of a ray.
1.2.1: Copying Segments and Angles
3
Concepts, continued
• A line segment is a part of a line that is noted by two
endpoints.
• An angle is formed when two rays or line segments
share a common endpoint.
• A constructed figure and the original figure are
congruent; they have the same shape, size,
or angle.
• Follow the steps outlined on the next few slides to
copy a segment and an angle.
1.2.1: Copying Segments and Angles
4
Copying a Segment Using a Compass
1. To copy AB , first make an endpoint on your paper. Label the
endpoint C.
2. Put the sharp point of your compass on endpoint A. Open the
compass until the pencil end touches endpoint B.
3. Without changing your compass setting, put the sharp point
of your compass on endpoint C. Make a large arc.
4. Use your straightedge to connect endpoint C to any point on
your arc.
5. Label the point of intersection of the arc and your segment D.
Do not erase any of your markings.
AB is congruent to CD.
1.2.1: Copying Segments and Angles
5
Copying a Segment Using Patty Paper
1. To copy AB , place your sheet of patty paper over the
segment.
2. Mark the endpoints of the segment on the patty paper. Label
the endpoints C and D.
3. Use your straightedge to connect points C and D.
AB is congruent to CD.
1.2.1: Copying Segments and Angles
6
Copying an Angle Using a Compass
1. To copy ∠A, first make a point to represent the vertex A on
your paper. Label the vertex E.
2. From point E, draw a ray of any length. This will be one side of
the constructed angle.
3. Put the sharp point of the compass on vertex A of the original
angle. Set the compass to any width that will cross both sides
of the original angle.
4. Draw an arc across both sides of ∠A. Label where the arc
intersects the angle as points B and C.
(continued)
1.2.1: Copying Segments and Angles
7
5. Without changing the compass setting, put the sharp point of
the compass on point E. Draw a large arc that intersects the
ray. Label the point of intersection as F.
6. Put the sharp point of the compass on point B of the original
angle and set the width of the compass so it touches point C.
7. Without changing the compass setting, put the sharp point of
the compass on point F and make an arc that intersects the
arc in step 5. Label the point of intersection as D.
8. Draw a ray from point E to point D.
Do not erase any of your markings.
∠A is congruent to ∠E.
1.2.1: Copying Segments and Angles
8
Copying an Angle Using Patty Paper
1. To copy ∠A, place your sheet of patty paper over the angle.
2. Mark the vertex of the angle. Label the vertex E.
3. Use your straightedge to trace each side of ∠A.
∠A is congruent to ∠E.
1.2.1: Copying Segments and Angles
9
Dr. Dambreville
THANKS FOR WATCHING!