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You will need scratch paper (not graph paper)

&

a straight edge today!

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Unit 6

Relationships with Triangles

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6.1 Perpendicular Bisectors and Angle Bisectors

Discover relationships between line segments and points of their perpendicular bisectors and explore angle bisectors. Write the equations of a perpendicular bisector given a line segment on a coordinate plane.

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On your Scratch Paper...

  1. With a straightedge, draw a line segment and label the endpoints A and B.
  2. Fold the paper so the endpoints match.
  3. Draw a line on the crease of the fold.
  4. Draw a point on that line, label point C.
  5. Draw segments AC and BC.
  6. Fold the paper again along the fold line. & write down your observations about the relationship of AC and BC.
  7. Place another point on the fold and label D and repeat steps 5-7 using point D.
  8. What is the relationship between Segment AB and Line CD?�

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Perpendicular Bisectors

  • Does the line bisect segment AB?
  • Is the line perpendicular to the segment?

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Example: Fill in any missing information we can conclude

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Example: Fill in any missing information we can conclude

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What do you know about this figure??

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On your Scratch Paper...

  • With a straightedge, draw an acute angle on the paper provided. Label vertex A.
  • Fold the paper so the sides of the angle match.
  • Draw a line on the crease of the fold.
  • Draw a point on that line, label point C.
  • Draw segments from point C perpendicular to each side of the angle. Label the intersection points R and S.
  • Fold the paper again along the crease line.
  • Write down your observations about the relationship of CR and CS.
  • Place another point on the fold and label D and repeat steps 5-7 using point D.
  • Did your observation in step 7 work using point D?��

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Example: Fill in any missing information we can conclude

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Example: Fill in any missing information we can conclude

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Writing Equations for Perpendicular Bisectors

On a coordinate plane you are given the line segment with endpoints P(-2, 3) and Q(4,1). Write the equation of the perpendicular bisector of the segment PQ.

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Writing Equations for Perpendicular Bisectors

On a coordinate plane you are given the line segment with endpoints D(5, -1) and E(-11, 3). Write the equation of the perpendicular bisector of the segment DE.