Triangle Similarity
Proportion
2 equal ratios.
Ratio
A comparison of 2 quantities with the same units. Must be fully simplified.
Similarity Statement
A statement that shows all the corresponding similar parts of 2 figures. For example: ABCD~EFGH.
Indirect Measurement
A technique that uses proportions to find a measurement when direct measurement is not possible.
True
Any two equilateral triangles are similar to each other.
False
Any two isosceles triangles are similar to each other.
Similarity Ratio
Between any two similar figures there is a ratio of any pair of corresponding sides. Once it is determined that two figures are similar, all of their pairs of corresponding sides have the same ratio.
AA Similarity Theorem
If 2 angles in one triangle are congruent to 2 angles in a second triangle, then the triangles are similar.
SSS Similarity Theorem
If 3 sides of one triangle are proportional to 3 sides in a second triangle, then the triangles are similar.
Dilation Rule
If a point A(x,y) follows a dilation whose scale factor is K, and the center of dilation is (0,0), then the dilation rule can be written as A' (x*k, y*k)
Cross Product Property
If a/b=c/d, then ad=bc.
SAS Similarity Theorem
If one pair of angles in 2 triangles are congruent, and the sides including the angle are proportional, then the triangles are similar.
Enlargement
Makes the pre-image bigger. The scale factor is bigger than 1.
Reduction
Makes the pre-image smaller. The scale factor is less than 1.
Altitude to the Hypotenuse Theorem
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
Scale Factor
The ratio of the image to the pre-image. The measure from the center to the image over the measure from the center to the pre-image.
Similar Polygons
The same shape but not the same size.
Center of Dilation
The single point from which we measure to create a dilation.
Dilation
When the entire pre-image undergoes a size change. The shape will NOT change.
