Practice Form K 7-2 Similar Polygons
The Correct Answer and Explanation is:
When studying similar polygons, the key concept is that the corresponding angles of two similar polygons are equal, and the lengths of their corresponding sides are proportional.
Example Problem:
Consider two similar polygons, Polygon A and Polygon B. The corresponding sides of Polygon A and Polygon B are in the ratio 2:3. If the side of Polygon A measures 4 cm, what is the corresponding side in Polygon B?
Step-by-Step Solution:
- Write the ratio of corresponding sides:
The ratio of the corresponding sides of similar polygons is constant. In this case, the ratio of the sides of Polygon A to Polygon B is given as 2:3. This means that for every 2 units in Polygon A, there are 3 corresponding units in Polygon B. - Set up a proportion:
Since the side in Polygon A is given as 4 cm, we can set up a proportion to find the corresponding side in Polygon B: Side of Polygon ASide of Polygon B=23\frac{\text{Side of Polygon A}}{\text{Side of Polygon B}} = \frac{2}{3}Side of Polygon BSide of Polygon A=32 Substituting the given value for the side of Polygon A: 4x=23\frac{4}{x} = \frac{2}{3}x4=32 where xxx represents the corresponding side in Polygon B. - Solve for xxx:
To solve for xxx, we cross-multiply: 4×3=2×x4 \times 3 = 2 \times x4×3=2×x This simplifies to: 12=2×12 = 2×12=2x Now, divide both sides by 2: x=122=6x = \frac{12}{2} = 6x=212=6 Therefore, the corresponding side in Polygon B is 6 cm.
Explanation:
The reason we can set up a proportion is that the properties of similar polygons tell us that their corresponding sides are proportional. By using the given ratio of the sides (2:3), we can determine the length of any missing corresponding side by cross-multiplying and solving for the unknown value. This same method applies to other geometric figures as well, as long as the polygons are similar, ensuring that their corresponding angles and side lengths maintain consistent ratios.
