UNIT 1 GLOSSARY
Congruent Segments- line segments that are congruent.
If line segment AB is congruent to line segment CD then AB=CD.
Congruent Angles- two angles that have the same measure.
If <ABC is congruent to < DEF then m<ABC=m<DEF.
Linear Pair- two angles that are adjacent and add up to 180 degrees.
No Notation
If <ABD and <DBE are a linear pair then m<ABD+m<DBC=180
Angle Bisector- a ray that divides an angle into two congruent angles.
No Notation
If Ray BD bisects <ABC then m<ABD and m<DBC are equal.
Segment Bisector- a ray segment or line that bisects a line segment.
No Notation
If ray DB bisects line segment AC then AB=BC.
Vertical Angle- two non-adjacent angles that are congruent formed by two intersecting lines
No notation
If <ABD and <CBE are vertical then m<ABD=m<CBE
Endpoint-the point at the ends of a line segment and at the start of a ray
No Notation
If the ray is called ray AB then the endpoint is A
If a line segment is called line segment CD then C and D are the endpoints.
If a line segment is called line segment CD then C and D are the endpoints.
Opposite rays
No Notation
If ray BA and ray BC are opposite rays then it forms Line AC
UNIT 2 GLOSSARY
Transversal
A transversal is a line that intersects two or more other lines at different points.
No notation
The transversal t crosses both lines m and n at two different points.
Concurrent Lines
Concurrent lines are three or more lines that intersect at the same point.
No Notation
Concurrent lines are three or more lines that intersect at the same point.
No Notation
In figures (a), (b), and (c), there are three or more lines that intersect at one central point.
Alternate Interior Angles
Alternate interior angles are both interior angles, not adjacent, and lie on opposite sides of the transversal.
No notation
Alternate interior angles are both interior angles, not adjacent, and lie on opposite sides of the transversal.
No notation
In these pictures, angles 4 and 5 are alternate exterior angles and therefore congruent. Angles 3 and 6 are also congruent because they are alternate exterior angles.
Alternate Exterior Angles
Alternate exterior angles are both exterior angles, not adjacent, and lie on opposite sides of the transversal.
No notation
Alternate exterior angles are both exterior angles, not adjacent, and lie on opposite sides of the transversal.
No notation
In this example, angles 1 and 8 are alternate exterior angles, which makes them congruent. Similarly, in the next picture angles 2 and 7 are alternate exterior angles, which makes them congruent.
Same Side Interior Angles
Same side interior angles are both interior angles, are not adjacent, and lie on the same side of the transversal.
No notation
Same side interior angles are both interior angles, are not adjacent, and lie on the same side of the transversal.
No notation
This picture shows that <JGH and <KHG are same side interior angles and that they are also supplementary.
Same side Exterior Angles
Same side exterior angles are both exterior angles, are not adjacent, and lie on the same side of the transversal.
No notation
Same side exterior angles are both exterior angles, are not adjacent, and lie on the same side of the transversal.
No notation
The diagram shows a pair of same side exterior angles and how they are supplementary to each other.
Corresponding Angles
Corresponding angles consist of one interior and one exterior angle, they are not adjacent, and they are on the same side of the transversal.
No notation
Corresponding angles consist of one interior and one exterior angle, they are not adjacent, and they are on the same side of the transversal.
No notation
This picture shows corresponding angles. <1 is the exterior angle and <2 is the interior angle. They also both lie on the same side of the transversal n.
Parallel Lines
Parallel lines are two or more coplanar lines that never intersect.
Notation: ll
Parallel lines are two or more coplanar lines that never intersect.
Notation: ll
These two lines will never cross because they have the same slope.
Transformation
A transformation is an operation that moves a geometric figure to produce a new figure.
No notation
A transformation is an operation that moves a geometric figure to produce a new figure.
No notation
In this figure, you can see the triangle being moved from quadrant to quadrant.
Isometry
An isometry is a transformation is congruent to the pre-image.
No notation
An isometry is a transformation is congruent to the pre-image.
No notation
Although the triangle has shifted positions, it maintained the same dimensions.
Image
The image is the new figure that is produced from a transformation.
No notation
The image is the new figure that is produced from a transformation.
No notation
In the example, the polygon F'E'A'D'C'B' had been translated from FEADCB.
Pre-Image
The pre-image is the original figure.
No notation
The pre-image is the original figure.
No notation
The pre-image triangle CBA was then reflected to form triangle C'B'A'.
Rotation
A rotation is a transformation that turns a figure around a fixed point.
No notation
A rotation is a transformation that turns a figure around a fixed point.
No notation
This triangle was rotated 90 degrees around the center of rotation.
Translation
A translation is transformation that moves each point of a figure the same distance in the same direction.
No notation
A translation is transformation that moves each point of a figure the same distance in the same direction.
No notation
In the picture, triangle ABC was translated 6 units right and 4 units down to form triangle A'B'C'.
Dilation
A dilation is a transformation in which a figure is enlarged or reduced around a given point.
No notation
A dilation is a transformation in which a figure is enlarged or reduced around a given point.
No notation
In this picture, the triangle was dilated by a scale factor of 2, which means it was enlarged.
Vector
Vectors are a way to notate a translation. It uses the change in x and y values to formulate a format of (h,k).
Notation: (h,k)
h is the horizontal change
k is the vertical change
Vectors are a way to notate a translation. It uses the change in x and y values to formulate a format of (h,k).
Notation: (h,k)
h is the horizontal change
k is the vertical change
In this picture, the point A was translated along the vector <-6,2> to point A'.
Mapping
Mapping is a way to notate a transformation. Mapping also uses the change in x and the change in y to formulate a format of (x,y) --> (x+h, y+k).
Notation: (x,y) --> (x+h, y+k)
h is the horizontal change
k is the vertical change
Mapping is a way to notate a transformation. Mapping also uses the change in x and the change in y to formulate a format of (x,y) --> (x+h, y+k).
Notation: (x,y) --> (x+h, y+k)
h is the horizontal change
k is the vertical change
The mapping rule for this picture is (x-6,y-5).
Line of Reflection
The line of reflection is the line of symmetry in a reflection or the perpendicular bisector of the segments that join each point of a figure to it's image.
No notation
The line of reflection is the line of symmetry in a reflection or the perpendicular bisector of the segments that join each point of a figure to it's image.
No notation
The line of reflection in this picture is x=-2. Each of the corresponding points has a midpoint on the line x=-2.
Center of Rotation
The center of rotation is the point around which a figure is rotated.
No notation
The center of rotation is the point around which a figure is rotated.
No notation
The triangle ABO was rotated clockwise around the point O to form triangle A'B'O.
Center of Dilation
The center of dilation is the point around which a figure is dilated.
No notation
The center of dilation is the point around which a figure is dilated.
No notation
In this picture, the triangle ABC was dilated around point O, which made triangle A'B'C'.
Composition Transformation
A composition transformation is the result when two or more transformations are combined.
No notation
A composition transformation is the result when two or more transformations are combined.
No notation
This picture shows the triangle ABC being reflected across the x axis and then translated to the left. Because there is more than one transformation, this picture shows a composition transformation.
Tessellation
A tessellation is a collection of figures that cover a plane with no overlaps or gaps.
No notation
A tessellation is a collection of figures that cover a plane with no overlaps or gaps.
No notation
This shows a regular tessellation consisting of diamond-like shapes and parallelograms. These shapes cover the whole plane with no gaps or overlaps.
Pure Tessellation
A pure tessellation is a collection of many of the same figure that covers a plane with no gaps or overlaps.
No notation
A pure tessellation is a collection of many of the same figure that covers a plane with no gaps or overlaps.
No notation
This picture shows a pure tessellation. The congruent leaves fit each other in a way that covers a plane perfectly with no gaps or overlaps.