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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