Visual Glossary
2A
Parallel Lines - Two or more co-planar lines with the same slope that never intersect. Symbol ||
Both the lines have the same slope, but the y-intercepts are different
Transversal - A line that intersects two or more lines at different points.
Symbol - none
Symbol - none
Concurrent lines - Lines that intersect in the same point.(There must be 3 or more).
Symbol - none
Symbol - none
All three of these lines intersect at the same point
Alternate interior angles - Two non-adjacent interior angles that are on opposite sides of the transversal.
Symbol - Alt. Int. <'s
Symbol - Alt. Int. <'s
Angle 1 and angle 2 are alternate interior angles
Alternate exterior angles - Two non-adjacent exterior angles that are on opposite sides of the transversal.
Symbol - Alt. Ext. <'s
Symbol - Alt. Ext. <'s
Angle FOA and angle DOE are alternate exterior angles
Same-side interior angles - Two non-adjacent interior angles on the same side of the transversal.
Symbol - SS Int. <'s
Symbol - SS Int. <'s
Both angles shown in the picture are same-side interior angles
Same-Side exterior angles - Two non-adjacent exterior angles on the same-side of the transversal.
Symbol - SS Ext. <'s
Symbol - SS Ext. <'s
Angle 1 and angle 2 are same side exterior angles
Corresponding Angles - Two non-adjacent angles (one is interior while one is exterior), that are on the same side of the transversal.
Symbol - none
Symbol - none
Both angles in this picture are corresponding angles
Vertical Angles - A pair of congruent angles whose sides form two pairs of opposite rays.
Symbol - none
Symbol - none
Angle 1 and angle 2 are vertical angles
Linear Pair - Two adjacent angles that are also supplementary.
Symbol - none
Symbol - none
Angle 1 and angle 2 are a linear pair
Perpendicular Lines - Lines that intersect at 90 degree angles.
Symbol - l
Symbol - l
The two lines in this picture intersect at right angles
2B
Transformation - An operation that changes a geometric figure, or the pre-image to form a new figure, or the image.
Symbol - none
Symbol - none
The blue pre-image is translated, rotated, dilated, and reflected to form the red image
Isometry - A transformation in which the image produced is congruent to it's pre-image.
Symbol - none
Symbol - none
The transformation above is an isometry, so the red image is congruent to the blue pre-image
Image - A figure after a transformation.
Symbol - none
Symbol - none
The red figure is the blue figure reflected over the red line
Pre-image - A figure before a transformation.
Symbol - none
Symbol - none
The blue figure is the red figure before it was reflected over the red line
Translation - A transformation that moves each point of a figure, the same distance, in the same direction.
Symbol - none
Symbol - none
ABC was translated to form A'B'C'
Mapping - (x,y) arrow (x+h,y+k), when h is the change in the x-axis while k is the change in the y-axis.
Symbol - none
Symbol - none
The mapping for this picture would be (x+6,y+0)
Vector notation - <h,k> h is the change in the x-axis, while k is the change in the y-axis.
Symbol - none
Symbol - none
The notation for this vector would be <-3,-4>
Reflection - A mirror image of a pre-image over a given line
Symbol - none
Symbol - none
The purple image is the orange image reflected over the black line
Line of Reflection - The line that a pre-image is reflected over. This line is also the perpendicular bisector of the segments that join each point of a pre-image to it's image.
Symbol - none
Symbol - none
The black line is the line of reflection
Rotation - A transformation in which a figure is turned around a fixed point.
Symbol - none
Symbol - none
The purple figure is rotated around the origin
Center of Rotation - The point that an object is rotated around.
Symbol - none
Symbol - none
Point x is the center of rotation
Composition transformation - The result of two or more combined transformations.
Symbol - none
Symbol - none
ABC is reflected over line l and translated via vector v.
Dilation - A transformation in which the pre-image is enlarged of reduced in size to form the image.
Symbol - none
Symbol - none
ABC is dilated to form A'B'C'
Center of dilation - The point that an object is dilated around.
Symbol - none
Symbol - none
Point O is the center of dilation
Tessellation - A collection of figures over a plane with no gaps or overlaps.
Symbol - none
Symbol - none
The figure above is a tessellation involving stars and parallelograms.
Scale Factor - A number that a pre-image's sides must be multiplied by to get those of the image.
Symbol - none
Symbol - none
The scale factor of this dilation is 1/2
Pure Tessellation - A collection of congruent figures that covers a plane with no gaps or overlaps.
Symbol - none
Symbol - none
This honeycomb is a pure tessellation.