1. Chapter 1: Tools of Geometry
1-7
Basic Constructions

2. Constructions
uses a straightedge and a compass to draw a geometric figure
what career would this be useful??
straightedge: ruler with no markings on it
compass: geometric tool used to draw circles and arcs

3. Construction #1: congruent segments
you will be given a segment to “copy”
steps:
draw a ray (with an endpoint)
measure the original segment with the compass
leave the compass open and draw an arc on your ray
label the point where the ray and arc intersect

4. Try it!! On your notes, there is a segment to copy
Work through the steps with me

5. Construction #2: congruent angles
you will be given an angle to copy
steps:
draw a ray like before
on the original angle open your compass and draw an arc that intercepts both sides of the angle
leave your compass open the same length and draw that arc on the ray
measure on the original angle the distance between the intersections
mark this length on the ray (I will show you)
connect the arc intersection with the endpoint of the ray

6. Try it!! On your notes, there is an angle to copy
Work through the steps with me

7. Bisectors perpendicular lines: bisector: cuts something in half
perpendicular bisector: a line/segment/ray that is perpendicular to the segment at its midpoint

8. Construction #3: perpendicular bisector
you will be given a segment
steps:
put the end of the compass on one end of the segment
open the compass to more than half of the segment and make an arc
keep that length and move your compass to the other endpoint and make another arc
draw a line between the intersections of the arc

9. Try it!! On your notes, there is a segment to bisect
Work through the steps with me

10. Construction #4: angle bisector
you will be given an angle
steps:
open your compass and draw an arc through both sides of the angle
measure the distance between intersections, and then open the compass a little larger
make an arc at that length in the middle of the angle from both intersections
draw a line from the vertex of the angle to the small arc intersection

11. Try it!! On your notes, there is an angle to bisect
Work through the steps with me

12. Example 4
KN bisects angle JKL. Solve for x and find the measure of angle JKN.

13. Homework!! p
1-8, 10-17, 22-24