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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

Sections 1.4- 1.7

By: Emily and Becca

1 4 geometry using paper folding
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
1 4 continued
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
1 5 special points in triangles
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
1 6 motion in geometry
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
1 6 continued
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 parallel1.6 Continued
1 6 continued1
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
1 6 continued2
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 image1.6 Continued

http://mrsdell.org/geometry/motion.html

1 7 motion in the coordinate plane
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)

1 7 continued
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)= (?,?)

practice problems
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.
more practice problems
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)
answers
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
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