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Constructing Perpendicular Bisectors and Lines

Learn construction techniques for constructing perpendicular lines and perpendicular bisectors. Explore terms, processes, conjectures, and examples.

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Constructing Perpendicular Bisectors and Lines

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  1. Constructing Perpendicular Bisectors and Lines Objective: Students will apply construction techniques to construct perpendicular lines and perpendicular bisectors.

  2. Terms Bisector – To cut in half, divided into 2 congruent segments or parts Perpendicular – When they intersect they form right angles

  3. Constructing a perpendicular Bisector Investigation pg 150

  4. Con’t

  5. Process • Place pointy end of compass and extend pencil end so it is more than halfway across segment, swing an arc above and below the segment • With same compass setting swing arc from second endpoint so it crosses the first arc both above and below the segment • Connect the intersections of the two arcs I call this making a piece of candy, because that is what it looks like

  6. Other Process What if you can’t swing an arc above or below the segment • Place pointy end on one endpoint and swing an arc that is greater than half the segment • Do same arc from other endpoint • Repeat step 1 and 2 with a different arc • Connect the two intersections

  7. Conjectures Perpendicular Bisector Conjecture If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints Convers of Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

  8. Median of a Triangle Median is a segment that connects the vertex of a triangle to the midpoint of the side opposite How would I construct this? Find the midpoint, How? Perpendicular bisector Connect the vertex and midpoint

  9. Midsegment of a Triangle Midsegment of a Triangle is a segment that connects two midpoints. How would you construct a midsegment? Find the midpoint of two sides Connect midpoints with a segment

  10. Example • Draw a triangle and label it ABC • From point a construct a median • From sides AB and AC construct a Midsegment

  11. Perpendicular LinesInvestigation pg 154

  12. Continues

  13. Perpendicular Lines Constructing a Line perpendicular to another line through a specific point. • Place pointy end on point not on the line • Swing an arc the will intersect the line in two places • Place point end on one intersection and swing arc on other side of line (do not change the size of the comp • Repeat with other intersection point • Connect original point with the intersection of the arcs

  14. Shortest Distance Conjecture The shortest distance from a point to a line is measured along the perpendicular segment for the point to the line

  15. Altitude The altitude or height of a triangle is a segment from a vertex perpendicular to the side opposite, this doesn’t necessarily bisect the side or angle

  16. Examples Pg 151 2,3 Pg 156 5

  17. Objective: Students will apply construction techniques to construct perpendicular lines and perpendicular bisectors. On a scale of 1 to 4 Do you feel we meet the objective for the day. If we did not meet the objective, what did we miss and how could I improve.

  18. Homework Pg 151 1,4,5,7,8,9 Pg 156 1-4

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