BASIC CONSTRUCTION

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

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

3. X C D ~ = A B 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

4. J A F D R S B G ~ = E C 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 H

5. A B ~ = 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 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. 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 Constructing a parallel line //

8. Construct a 30 degree angle Given: Line AB A B

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

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 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??? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?