Ratios and proportions Flashcards
Proportion
an equation that states that 2 ratios are equal
geometric mean
the geometric mean of 2 positive numbers A & B is the positive # x that satisfies a/x = x/b and x= the square root of ab
scale
a ratio that describes how the dimensions in the drawing are related to the actual dimension of the object
similar polygons
two polygons are similar if corresponding angles are congruent and corresponding side lengths are proportional
scale factor
the ratio of the lengths of 2 corresponding sides of 2 similar polygons
If 2 polygons are similar then the ratio of their perimeters is equal to the ratios of their corresponding side lengths =
Theorem 6.1 Perimeters of similar polygons
If 2 polygons are similar the the ratio of any 2 corresponding lengths in the polygons is equal to the scale factor of the polygons.
Corresponding lengths in similar polygons
If 2 angles of 1 triangle are congruent to 2 angles of another triangle then the 2 triangles are similar
AA Postulate
*scale factor is never a decimal
helpful
*If it starts in decimals keep decimals
helpful
*AA is only for triangles
helpful
If the corresponding side lengths of 2 triangles are proportional then the triangles are similar
SSS
if an angles 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
SAS
If a line is parallel of a triangle intersects the other 2 sides then it divides the 2 sides proportionally
Theorem 6.4 Triangle Proportion Theorem
If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally
Theorem 6.6
