2. Copying Segments and Angles Adapted from Walch Education

3. 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 Angles2

4. 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 Angles3

5. 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 Angles4

6. 5 Copying a Segment Using a Compass 1.To copy, 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. is congruent to.

7. 1.2.1: Copying Segments and Angles6 Copying a Segment Using Patty Paper 1.To copy, 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. is congruent to.

8. 1.2.1: Copying Segments and Angles7 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)

9. 1.2.1: Copying Segments and Angles8 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.

10. 1.2.1: Copying Segments and Angles9 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.

11. THANKS FOR WATCHING! Ms. Dambreville