1. Constructions

2. Vocabulary
Congruent-the same measurement
Construct-to create
Straightedge-any object you can use to make a straight line
Compass-an instrument used to create circles or parts of circles
Arc-part of a circle that can be drawn with a compass

3. Constructing Line Segments
Draw a line segment and label it AB
A B

4. Constructing Line Segments
Use a straightedge to draw Ray PS so it’s longer than AB
A B
P S

5. Constructing Line Segments
Place the endpoint in the circle of the safety compass at A and the pencil point on B and tighten down. Draw an arc.
A B
P S

6. Constructing Line Segments
Keep the same setting on the compass and place the point at P. Draw an arc that intersects PS at a new point Q.
A B
P Q S

7. Constructing Congruent Angles
Draw an angle and label it PQR P Q R

8. Constructing Congruent Angles
Use a straightedge to draw Ray ST P Q R
S T

9. Constructing Congruent Angles
Place the point in the circle of the safety compass at vertex Q. Set your measurement to 2 cm.Draw an arc that intersects both sides of PQR to make points X and Y. X Q Y

10. Constructing Congruent Angles
Keeping the same setting, place the point at S and draw an arc that intersects ST. Label the intersection Point A. X Q Y
S A

11. Constructing Congruent Angles
Place the compass so that the point is at X and first drawing hole is at Y. Keep that setting and place the point at A. Draw an arc that intersects the arc you drew in Step 3. Label that intersection Point M. X Q Y
S A

12. Constructing Congruent Angles
With the straightedge, draw Ray SM. Angle MST is congruent to Angle PQR.

13. Compass Questions How does the compass work in copying a line segment?
Explain how the compass works in copying an angle.

14. Bisecting Line Segments
Draw a line segment and label it CD

15. Bisecting Line Segments
Place the point of the compass at C. Extend the runner until the first drawing hole is more than halfway to D and set it. Draw an arc “above” and “below” CD.

16. Bisecting Line Segments
Keeping the same setting, place the point on D and draw another arc “above” and another “below” for two new points Q and R.

17. Bisecting Line Segments
With a straightedge, draw the line segment determined by the two new points. This will intersect the original line. Name the intersection Point M.

18. What do you think bisect means?
What type of angles are formed by perpendicular segments?

19. Bisecting Angles
Draw an angle and label it Angle ABC.

20. Bisecting Angles
Place the point of the compass at B and draw an arc that intersects both sides of the angle. Label the points of intersection X and Y.

21. Bisecting Angles
Place the point of the compass at X and move the runner to a length more than halfway to Y. Draw an arc in the interior of Angle ABC.

22. Bisecting Angles
Keep that same setting and place the point at Y and draw an arc that intersects the arc you just drew. Label the intersection T.

23. Bisecting Angles
With a straightedge, draw Ray BT, this is the bisector of Angle ABC.