Two numbers are claimed to be comparable if they space the very same shape. In an ext mathematical language, two figures are similar if their equivalent angles room congruent , and the ratios the the lengths of their equivalent sides space equal.

This usual ratio is called the scale factor .

The price ∼ is provided to show similarity.




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example 1:

In the number below, pentagon A B C D E ∼ pentagon V W X Y Z .

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(Note the the order in which you write the vertices matters; because that instance, pentagon A B C D E is not similar to pentagon V Z Y X W .)


instance 2:

The 2 cylinders room similar. Uncover the range factor and the radius that the 2nd cylinder.

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The height of the cylinder top top the appropriate is 1 3 the height of the cylinder top top the left. So, the scale aspect is 1 3 .

To obtain the radius of the smaller cylinder, divide 1.8 by 3 .

1.8 ÷ 3 = 0.6

So, the radius of the smaller cylinder is 0.6 cm.


keep in mind that a two-dimensional number is similar to an additional if the second can be acquired from the first by a sequence of rotations , reflections , translations , and also dilations .




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example 3:

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In the number above, the hexagon A 1 B 1 C 1 D 1 E 1 F 1 is flipped horizontally to get A 2 B 2 C 2 D 2 E 2 F 2 .

climate hexagon A 2 B 2 C 2 D 2 E 2 F 2 is interpreted to acquire A 3 B 3 C 3 D 3 E 3 F 3 .

Hexagon A 3 B 3 C 3 D 3 E 3 F 3 is dilated through a scale factor of 1 2 to obtain A 4 B 4 C 4 D 4 E 4 F .

note that

A 1 B 1 C 1 D 1 E 1 F 1 ∼ A 2 B 2 C 2 D 2 E 2 F 2                                                               ∼ A 3 B 3 C 3 D 3 E 3 F 3 ∼ A 4 B 4 C 4 D 4 E 4 F 4 .

the is, all 4 hexagons room similar. (In fact, the very first three space congruent.)


instance 4:

consider pentagon ns Q R S T ~ above a name: coordinates plane.

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A rotation by 180 ° around the beginning takes the pentagon come ns " Q " R " S " T " .

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Now, a dilation about the beginning by a scale factor 2 takes the pentagon ns " Q " R " S " T " to p " " Q " " R " " S " " T " " .

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keep in mind that p Q R S T ∼ p " Q " R " S " T " ∼ ns " " Q " " R " " S " " T " " . The is, all three pentagons are similar. (And the an initial two are congruent.)