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Tools of Geometry Toolkit 1.5-1.6

Tools of Geometry Toolkit 1.5-1.6. Today’s Goals: To investigate perpendicular lines & bisectors. To use the midpoint and distance formulas. Perpendicular Lines. Two lines that intersect to form right angles. Symbol: means “is perpendicular to”. Bisectors.

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Tools of Geometry Toolkit 1.5-1.6

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  1. Tools of Geometry Toolkit 1.5-1.6 Today’s Goals: To investigate perpendicular lines & bisectors. To use the midpoint and distance formulas.

  2. Perpendicular Lines • Two lines that intersect to form right angles. • Symbol: means “is perpendicular to”

  3. Bisectors Perpendicular bisector (of a segment) • A line, segment, or ray that is perpendicular to a segment at its midpoint • Bisects segment into two congruent segments.

  4. Bisectors Angle bisector • A ray that divides an angle into two congruent coplanar angles • Endpoint is at the angle’s vertex.

  5. Ex.1: Finding Angle Measures • KN bisects JKL • mJKN = 5x – 25 • mNKL = 3x + 5. • Solve for x and find mJKN.

  6. Why do we need the distance formula?

  7. The Distance Formula • 1st coordinate (x1, y1) • 2nd coordinate (x2, y2)

  8. Ex.2: Finding Distance • Find the distance between T(5,2) and R(- 4,-1). • Write answer in simplest radical form.

  9. B A Ex.3:Finding the MidpointAB has endpoints A(4,3) and B(8,5)

  10. The Midpoint FormulaFind the “average” of each coordinate!! • 1st coordinate (x1, y1) • 2nd coordinate (x2, y2)

  11. Ex.4:Finding an EndpointThe midpoint of AB is M(3,4). One endpoint is A(-3,2). Find the coordinates of the other endpoint B. M Let the coordinates of B be (x2, y2) A

  12. Geometry Book P29 2-22E, 29-33 P38 10-12 P46 2,16,20,24,26,30

  13. 3-D Coordinate System

  14. CHALLENGE PROBLEMS Pg. 48 #60-63 • In a three-dimensional coordinate system, the distance between two points (x1, y1, z1) and (x2, y2, z2) can be found using this extension of the Distance Formula.

  15. 3-D Points#60 A = ________ B = ________ C = ________ D = ________ E = ________ F = ________ G = ________

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