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Sections 1.4- 1.7

Sections 1.4- 1.7. By: Emily and Becca. Perpendicular Lines- Two lines that intersect to form a right angle. Parallel Lines- Two coplanar lines that do not intersect. 1.4 Geometry using Paper Folding. Segment Bisector- A line that divides a segment into two congruent parts.

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Sections 1.4- 1.7

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  1. Sections 1.4- 1.7 By: Emily and Becca

  2. Perpendicular Lines- Two lines that intersect to form a right angle. Parallel Lines- Two coplanar lines that do not intersect 1.4 Geometry using Paper Folding

  3. Segment Bisector- A line that divides a segment into two congruent parts. Conjecture- A statement that you believe to be true. An educated guess based on observations Midpoint- the point where a bisector intersects a segment. Perpendicular Bisector- A bisector that is perpendicular to a segment Angle Bisector- A ray or line that divides an angle into two congruent angles 1.4 Continued

  4. Inscribed Circle- A circle that is inside a triangle that just touches the three sides. Circumscribed Circle- A circle that is outside the triangle and contains all three vertices. 1.5 Special Points in Triangles

  5. 1.6- Motion in Geometry • Rigid Transformations- Transformations that do not change the size or shape of a figure • Preimage- The original figure before any transformations occur • Image- The transformed figure

  6. Translation- In a Translation, every point of a figure moves in a straight line, and all points move the same distance in the same direction. The paths of the points are always parallel 1.6 Continued

  7. 1.6 Continued • Rotation- Every point of a figure moves around a given point known as the Center of Rotation. All points move the same angle measure

  8. Reflection- A transformation in which every point of the preimage is moved across a line known as the mirror line so that the mirror is the perpendicular bisector of the segment connecting the point and its image 1.6 Continued http://mrsdell.org/geometry/motion.html

  9. 1.7 Motion in the Coordinate Plane • By applying algebraic operations to the coordinates of a point, you can relocate it on the coordinate plane. • Ex: Preimage: A(2,3) Image A’(4,7) Transformation Notation: T(x,y)= (x+2,y+4)

  10. 1.7 Continued • Horizontal and Vertical Coordinate Translations Horizontal translation of H units: H(x,y)= (?,?) Vertical translations of V units: V(x,y)= (?,?) • Reflection Across the X or Y axis Reflection across the X axis: M(x,y)= (?,?) Reflection across the Y axis: N(x,y)= (?,?) • 180 Rotation about the Origin R(x,y)= (?,?)

  11. Practice Problems • 1.4 : Suppose that M is the angle bisector of <BAC and that m<CAJ = 15. Find m<BAJ and m<BAC • 1.5: Find the measure of angle CBE and EBD. AE bisects angle CBD.

  12. More Practice Problems • 1.6: Reflect the figure across the given line. • 1.7:Describe the result of applying each rule to a figure • F(x,y) = (x+7,y) • A(x,y) = (x-6, y+7)

  13. Answers: • 1.4: m<BAJ = 15, m<CAB= 30 • 1.5: m< CBE= 1 m< EBD= 1 • 1.6: • 1.7: translation 7 units to the right • Translation 6 units to the left and 7 up

  14. The End

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