sections 1.4- 1.7 by: emily and becca. 1.4 geometry using paper folding perpendicular lines- two...
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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 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
1.5 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.
1.6- 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
• 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 Continued
• 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 imagehttp://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 TranslationsHorizontal translation of H units: H(x,y)= (?,?) Vertical translations of V units: V(x,y)= (?,?)
• Reflection Across the X or Y axisReflection across the X axis: M(x,y)= (?,?)Reflection across the Y axis: N(x,y)= (?,?)
• 180 Rotation about the OriginR(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.
j
B
C
A
-11x+3
4x-12A E
C
D
B
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
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