### Similar Polygons

**Similar polygons** room two polygons with the same shape, but not the same size. Comparable polygons have corresponding angles that room **congruent**, and corresponding sides that are **proportional.You are watching: The polygons are similar but not**

These polygons room not similar:

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All the matching angles room congruent because the shapes are rectangles.

Let’s view if the sides are proportional. (dfrac812=dfrac23) and also (dfrac1824=dfrac34). (dfrac23
eq dfrac34), therefore the sides are ** not** in the same

**proportion**, and also the rectangles space

**similar.**

*not*Example (PageIndex2)

(Delta ABCsim Delta MNP). The perimeter the (Delta ABC) is 150, (AB=32) and also (MN=48). Uncover the perimeter that (Delta MNP).

**Solution**

From the similarity statement, (AB) and also (MN) are equivalent sides. The scale element is (dfrac3248=dfrac23) or (dfrac32). Delta ABC) is the smaller sized triangle, so the perimeter of (Delta MNP) is (dfrac32(150)=225).

Example (PageIndex3)

Suppose (Delta ABCsim Delta JKL). Based on the similarity statement, which angles are congruent and which sides room proportional?

**Solution**

Just like in a congruence statement, the congruent angle line up within the similarity statement. So, (angle Acong angle J), (angle Bcong angle K), and also angle Ccong angle L). Write the sides in a proportion: (dfracABJK=dfracBCKL=dfracACJL). Note that the proportion might be written in different ways. For example, (dfracABBC=dfracJKKL) is additionally true.

Example (PageIndex4)

(MNPQ sim RSTU). What are the values of (x), (y) and also (z)?

Figure (PageIndex4)**Solution**

In the similarity statement, (angle Mcong angle R), therefore (z=115^circ). Because that (x) and (y), collection up proportions.

See more: 2004 Pontiac Grand Prix Power Steering Problems, Power Steering Issues

(dfrac1830=dfracx25 qquad dfrac1830=dfrac15y)

(450=30x qquad 18y=450)

(x=15qquad y=25)

Example (PageIndex5)

(ABCDsim AMNP). Discover the range factor and the size of (BC).

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