Create an account
In a proportion, the denominator of the first equation and the numerator of the second equation
In a proportion, the numerator of the first equation and the denominator of the second equation
Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding lengths (same scale factor)
Angle-Angle similarity postulate: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
Side-Side-Side similarity theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar
Side-Angle-Side similarity theorem: If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar
Triangle Proportionality Theorem and Converse
A line is parallel to one side of a triangle IFF it intersects the other two sides proportionally
Transversal Similarity Theorem
If three parallel lines intersect two transversals, then they divide the transversals proportionally
Angle Bisector Similarity Theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides
Cross Product Property
In a proportion, the product of the extremes equals the product of the means: if a/b = c/d (and b and d both not 0) then ad = bc
Given a proportion, the reciprocals of the ratios are equal: if a/b = c/d then b/a = d/c
Given a proportion, if you interchange the means (or the extremes!), then you form another true proportion: if a/b = c/d then a/c = b/d
Given a proportion, if you add the value of the denominator to the numerator, then you form a true proportion: if a/b = c/d then (a+b)/b = (c + d)/d
Two polygons in which the corresponding angles are congruent and corresponding side lengths are proportional; similar polygons have the same shape, but not necessarily the same size; angles are congruent and sides are in proportion (have a common scale factor)
Please allow access to your computer’s microphone to use Voice Recording.
Having trouble? Click here for help.
We can’t access your microphone!
Click the icon above to update your browser permissions and try again
Reload the page to try again!Reload
Press Cmd-0 to reset your zoom
Press Ctrl-0 to reset your zoom
It looks like your browser might be zoomed in or out. Your browser needs to be zoomed to a normal size to record audio.
Please upgrade Flash or install Chrome
to use Voice Recording.
For more help, see our troubleshooting page.
Your microphone is muted
For help fixing this issue, see this FAQ.
Star this term
You can study starred terms together