How do you know if two polygons are similar?

1 answer:

7 0

Any two polygons are similar if their corresponding angles are congruent and the measures of their corresponding sides are proportional: In the figure above the ratio or the scale factor of the quadrilateral to the left versus the quadrilateral to the right is ½. ( or the easy way same shape, same side)

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The hypotenuse of a 45°-45°-90° triangle measures 10 sqrt 5 in. What is the length of one leg of the triangle?

olga nikolaevna [1]

There is this specific ratio for 45-45-90 triangles where the length of the hypotenuse is radical 2 times as long as a leg. With this in mind, we can create an equation where the length of one leg is represented with the variable x.

x $\sqrt{2}$ = 10 $\sqrt{5}$
divide both sides by $\sqrt{2}$
x = 10 $\sqrt{5}$ / $\sqrt{2}$
x = 10 $\sqrt{10}$ /2
x = 5 $\sqrt{10}$

The length of one leg is 5 $\sqrt{10}$

3 0

4 years ago

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