1. BY WENDY LI AND MARISSA MORELLO
BASIC CONSTRUCTION
BY WENDY LI AND MARISSA MORELLO
You will need…..
Straight edge
(ID card works)
A Compass

2. Aim: How to use a compass and straightedge to form basic constructions?
Homework: Complete Worksheet
Do Now: Construct the angle bisector of <ABC A B C

3. Constructing a Congruent Line Segment
Given: AB
1) With a straightedge, draw any line, CD, and mark a point X on it.
2) On AB, place the compass so that the point A and the pencil point is at B.
3) Keeping the setting on your compass, place the point at X and draw an arc intersecting CD at Y
Conclusion: XY AB ~ = Y C D X A B

4. Constructing a Congruent Angle
Given: <ABC
1) Draw point D, and draw a line, RS, going through it
2) Put point of compass on B of <ABC and draw an arc going through sides BA and BC. Label the points F and E.
3) Using the same radius and point D as the center, draw an arc that intersects DS. Label it GJ
4) Using the compass, measure the distance between E and F. Then with G as a center and a radius whose length is EF, draw an arc that intersects GJ at H.
5) Draw DH.
Conclusion: <ABC <HDS ~ = J G H A B C E F D R S

5. Constructing a Perpendicular Bisector
Given: Line Segment AB
1) Open compass, to a length more than one half of the length AB.
2) Using point A as a center, draw one arc above and one arc below AB
3) Using the same radius and point B as a center, draw an arc above and an arc below AB that intersects the first pair of arcs.
4) Use a straightedge to draw a line, CD, that intersects the set of arcs and AB at E
Conclusion: CD AB
AE EB ~ = C A B E D

6. Constructing an Angle Bisector
Given: <ABC
1) With B as a center and any radius, draw an arc that intersects BA and BC. Label the intersecting points D and E.
2) With D and E as centers, draw arcs that intersect at F, using equal radii.
3) Draw BF
Conclusion: <ABF <CBF ~ = A D F B E C

7. Constructing a parallel line
1) Through P, draw any line intersecting AB at R. Let S be any point on the ray opposite PR
2) With R as a center, draw an arc that goes through RP and AB. Using the same radius and P as a center draw an arc that intersects Ray PS at S.
3) Measure the distance between the intersecting points of the arc at R .Using S as a center and the distance measured before as the radius, draw an arc that intersects the other arc.
4) Draw Line CD through point P, intersecting the arc also.
Conclusion: CD AB //

8. Construct a 30 degree angle Given: Line AB

9. 2. Construct a right isosceles triangle when given line segment AB

10. 3. The reason that line L is parallel to line m is…
when two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel
when two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

11. The diagram below shows the construction of
the perpendicular bisector of AB.
Which statement is not true?
[A] AC + CB = AB
[B] AC = CB
[C] CB = AB
[D] AC = 1/2AB

12. The construction below shows a perpendicular from a point off the line
The construction below shows a perpendicular from a point off the line. The reason that PA is perpendicular to line l is  
                                                                                      
the locus of points equidistant from two given points is a perpendicular bisector of the segment formed by the two points.
perpendicular lines always form right angles.
two congruent triangles are formed illustrating SAS.
the locus of points equidistant from a given point is a circle.

13. ? ? ? ? ?
ANY QUESTIONS??? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?