Once we know that two figures are similar, we also know additional information about certain measurements involving these figures.

Ratio of Lengths: Perimeters, Altitudes, Medians, Diagonals, Angle Bisectors

If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio.
(Note that these are all "length" measurements.)
In similar figures, if the ratio of any of these corresponding lengths is expressed as aoverb,
then the ratio of the other corresponding lengths can also be expressed as aoverb.

Example: If the corresponding sides of two similar triangles are in the ratio 2:5, what is the ratio of their perimeters?
Answer: 2:5

 


Ratio of Areas (square units)

If two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
(Note that area is not a "length" measurement - it is a surface "area" measurement.)

In similar figures, if the ratio of two corresponding sides (or other lengths) is expressed as aoverb,
then the ratio of the ares can be expressed asa2overb2.

Example: If the corresponding sides of two similar triangles are in the ratio 3:7, what is the ratio of their areas?
Answer: 9:49

 

 

Ratio of Volumes (cube units)

If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.
(Note that volume is not a "length" measurement - it is a 3-D measurement.)

In similar figures, if the ratio of two corresponding sides (or other lengths) is expressed as aoverb,
then the ratio of the volumes can be expressed asa3overb3.

Example: If the sides of two cubes are in the ratio 2:3, what is the ratio of their volumes?
Answer: 8:27



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