Quotients of Sides Within Similar Polygons

SIMILAR POLYGONs

By SCOTTIE GAMELON

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​Study the polygons in figure below and answer the questions that follow.

​ 1. Describe the figures. What can you say about their shapes and sizes?

2. ​ Find the ratios of the corresponding sides of the smaller figure to the bigger figure.

3. How are the corresponding angles related?

4. Are the two polygons similar or congruent? Explain your answer.​

• ​Two polygons are similar if and only if their corresponding sides are proportional.

• Similar polygons have the same shape but different sizes.

• The symbol ~, which is read as " is similar to, " indicates that two polygons are similar.

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​SIMILAR POLYGONS

​ABCD ~ EFGH

Corresponding angles

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​Corresponding sides

​Example 1: In figure 1, isosceles trapezoid LMNO correspond to isosceles trapezoid WXYZ. Determine the corresponding angles and sides. Is isosceles trapezoid LMNO similar to isosceles trapezoid WXYZ? If so, write a similarity statement and determine the ratio of similarity.

​​Corresponding angles:

​

​​Corresponding sides:

​Therefore, the ratio of similarity is 3 or 3: 1 .

​Example 2: The polygons in each pair are similar, that is, KIND ~ LOVE, and RSPQ ~ NKLM. Determine the ratio of similarity and th length of the indicated side.

​Solution:

​Solve for KI.

​Thus, KI =9

​Solution:

​Solve for NM.

GROUP ACTIVITY

​Group 1 & 2: Find the value of x and the length of the indicated side. The polygons in each pair are similar.

​Group 3 & 4: State whether each pair of polygons is similar or not similar. If similar, write the similarity statement and determine the ratio of similarity?