Sections 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 image ry/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= : 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