Parallel & Perpendicular Lines
Parallel lines have this special relationship between their slopes.
Two angles that sit perfectly across from each other in an intersection.
What are vertical angles?
This "click and drag" transformation shifts a figure horizontally, vertically, or both.
What is translation?
This postulate allows us to say two triangles are congruent if two sides and the angle between them in one triangle are congruent to two sides and the included angle in the other triangle.
What is SAS?
This property tells us that if two quantities are equal to each other, one can be plugged in in place of the other in any equation.
Perpendicular lines have this two-part special relationship between their slopes.
What is negative reciprocal?
Two angles that sit next to each other and form a straight line.
What is a linear pair?
The rule (x,y) -> (x+2,y-1) corresponds to this transformation in this specific direction.
What is a translation right two units and down one unit?
This is the only congruence postulate we could use if we have no information about any angles in either triangle.
What is SSS?
This vocab word is useful for the "reasons" column whenever we're using a piece of information that the problem tells us up front.
What is "given"?
Given a line y=-4x+1, this value would represent the slope of a line parallel to it.
What is -4?
Any two angles that add up to 180 degrees.
What are supplementary angles?
The rule (x,y) -> (-x,y) corresponds to this transformation in this specific direction.
What is a reflection over the y-axis?
This is the only congruence theorem we have that only works on right triangles.
What is HL?
This property tells us that if two things are equal to the same thing, they are equal to each other. (That is, if a=b and b=c, a=c).
What is the transitive property?
This form of a line allows us to plug in the coordinates of a point we know as well as the slope of the line to easily make the equation of the line: y-y1=m(x-x1).
In a parallel line/transversal diagram, these are two angles that occupy the same relative location in two different intersections.
What are corresponding angles?
The rule (x,y) -> (-y,x) corresponds to this transformation in this specific direction.
What is a rotation 90 degrees counterclockwise?
When proving two triangles are congruent, if the diagram includes a shared side (part of both triangles), this is the reason we use when including this side as an "S" in our chosen postulate.
What is the reflexive property?
This property tells us that everything is equal (or congruent) to itself.
What is the reflexive property?
Given a line y=7x-5, this value would represent the slope of a line perpendicular to it.
What is -1/7?
These two angles sit between the parallel lines but on opposite sides of the transversal.
What are alternate interior angles?
This is the only transformation we've (briefly) discussed that is NOT a rigid motion and therefore does NOT produce congruent figures.
What is a dilation?
This famous combination of S's and A's is NOT one of our postulates and does NOT guarantee congruent triangles.
What is SSA?
What is "property of equality"?