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Sections 1.4- 1.7 PowerPoint PPT Presentation


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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 parallel

1.6 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 image

1.6 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


Sections 1 4 1 7

The End


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