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

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

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

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

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

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

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 //

Construct a 30 degree angle Given: Line AB

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

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.  

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

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.

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