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Aim: How do we use a compass and straightedge to perform all compass constructions?

Aim: How do we use a compass and straightedge to perform all compass constructions?. DO NOW! – Using the given line, construct a 45 degree angle. A B. Congruent Line Segments:. Draw line segment AB and an external point X. Measure AB with compass.

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Aim: How do we use a compass and straightedge to perform all compass constructions?

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  1. Aim: How do we use a compass and straightedge to perform all compass constructions? DO NOW! – Using the given line, construct a 45 degree angle. AB

  2. Congruent Line Segments: • Draw line segment AB and an external point X. • Measure AB with compass. • Keeping the distance place the center at X and draw the same arc. Label line XY. Practice: A B X

  3. Congruent Angles • Draw line ST. • Given angle PQR put center at Q and draw an arc that intercepts both rays of the angle. Name these points X and Y. • Keeping the distance, put center on S and draw the same arc intersecting ST. Label this A. • Place compass so both tips are on X and Y and draw arc. Keeping the same distance place the steel tip at A. Draw an arc that intersects the arc you drew in the previous step. Label this point M. • Draw QM. P Practice: Q R

  4. Equilateral Triangle • Given line AB, use A as center and measure with compass. Draw arc on B. • Keeping same distance and using B as the center construct BC. • Do the same from point A • Label C where arcs intersect. Draw line segments AC and BC. Practice: A B Perpendicular Bisector • Given line AB, open compass to be more than half of AB. • Using A as center, draw an arc above and below AB. Do the same using B as the center. • Draw line CD through the points where the arcs intercept. Practice: A B

  5. Angle Bisector • Given angle ABC, draw arc that intercepts both rays of the angle at points D and F. • Keeping the same distances, draw an arc from D and the F that intersect at E. • Draw BE. A Practice: B C Median of Triangle • Given triangle ABC, construct RS, the perpendicular bisector of BC. • Label M where line RS intersects side BC. Draw AM. Practice: A B C

  6. Perpendicular line to a given line through a point on the line • Given line AB with point P on the line, using P as center, draw an arc that intercepts line AB at points C and D. • Using C as the center open compass to be more than half of CD and draw arc. Do the same using D as the center and label where they meet, Point E. • Draw line EP Practice: A P B -What if P is an external point? Draw diagram.

  7. Parallel Line to Given Line Through External Point: • Given line AB and external point P, draw line through P intersecting AB at R that will be used as the transversal. (Let S be any point on the ray opposite PR.) • From points P and R, construct congruent corresponding angles. Practice: P A B

  8. Group Work / Pair Share -Given the following circle P, and AB as the diameter: • Construct the perpendicular bisector of AB to the top and bottom of circle P and label it RS where it meets the circle. • Draw triangle PRB and find the median PM. • Construct a line parallel to AB through point R. (You may extend RS.) • State the relationship between this parallel line and circle P. A B P

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