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## PowerPoint Slideshow about ' Sections 1.4- 1.7' - abena

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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 FoldingSegment 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 ContinuedInscribed 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 Triangles1.6- 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

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 Continued1.6 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

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

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

- 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

- 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

- 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:

- 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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