A rule that says that if two triangles have two pairs of congruent corresponding angles, then the triangles are totally BFFs—err, similar.
Center Of Dilation
Like the flame that moths just can't stay away from, the center is the point of a dilation where the rays that connect corresponding vertices of similar polygons all intersect.
A transformation that changes a shape into either a miniature or expanded version of the same shape. Optimus Prime rejected Dilate's application to join the Transformers because it was pretty obvious who he was, regardless of which form he took. He couldn't sneak up on a Decepticon to save his life.
Just like setting the Xerox machine to copy at 150%, an enlargement is when your dilation results in a bigger shape than you started with. The scale factor of the dilation will be more than one.
A shape post-dilation. May or may not be grotesquely over- or under-sized.
A line segment that connects the midpoints of two sides of a triangle. It's half the length of and parallel to the third side.
A shape, pre-dilation, with a predilection for preposterous predictions.
A mathematical statement that establishes equality between two ratios. By calling themselves proportional, ratios proclaim to all that they are equivalent and deserve a nice crusty baguette just as much as the next ratio. "Liberté, égalité, geometré," as Victor Hugo so wisely wrote.
A comparison of two quantities, written as a fraction (½), with the word "to" in between (3 to 5), or with a colon (9:2). Not to be confused with CSI: Miami's Horatio
Like setting the Xerox machine to copy at 50%, when a dilation's scale factor is less than one, it gives you a smaller shape than the one you started with.
The ratio that tells how much the size changes in a dilation. It compares the lengths of the sides of the preimage and image, as well as how far away each one is from the center of dilation. It is NOT related to weigh-ins at your local weight loss support center.
A rule stating that if two triangles have proportional adjacent sides and the angles between them are congruent, then the triangles are similar.
Yet another rule. This one says that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.
Surely you've got this one by now. Shapes with congruent corresponding angles and proportional corresponding sides.
There may be more than one way to skin a cat, but there's only one way to transform a shape and result in a similar shape. Similarity transformation, a.k.a. dilation, changes a shape's size, either shrinking it or enlarging it.
Triangle Proportionality Theorem
This theorem claims that if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections. It seems pretty sure of itself, so we'll trust it.
Triangle Midsegment Theorem
This rule is all about the midsegments…seriously. All it does is sit around all day and define the midsegment (the line segment connecting the midpoints of two sides of a triangle) as being half the length of and parallel to the third side of a triangle.