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Similar Triangles Terms

Get down with the lingo

Angle-Angle Postulate

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.

Dilation

Using a scale factor to produce a new, proportional image from an original. The new shape can be bigger or smaller, but it has to be in scale. This is not to be confused with the process the optometrist uses on your pupils to blind you for 6 hours.

Enlargement

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 1.

Image

A shape post-dilation. May or may not be grotesquely over- or under-sized.

Midsegment

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.

Preimage

A shape, pre-dilation, with a predilection for preposterous predictions.

Proportion

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.

Ratio

A comparison of two quantities, written as a fraction (), with the word "to" in between (3 to 5), or with a colon (9:2). Not to be confused with CSI: Miami's Horatio.

Reduction

Like setting the Xerox machine to copy at 50%, when a dilation's scale factor is less than 1, it gives you a smaller shape than the one you started with.

Scale Factor

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.

Side-Angle-Side Postulate

A rule stating that if two triangles have proportional adjacent sides, and the angles between them are congruent, then the triangles are similar.

Side-Side-Side Postulate

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.

Similar

Surely you've got this one by now. Shapes with congruent corresponding angles and proportional corresponding sides.

Similarity Transformation

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.

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