"Similar polygons"

Similar Polygons

• Definition: Similar polygons are shapes that have the same shape but may differ in size.
• Key Concept: In similar polygons, the ratios of the lengths of corresponding sides are equal.
  • If polygon A is similar to polygon B, then:
  • $\frac{Length \ of \ Side \ A1}{Length \ of \ Side \ B1} = \frac{Length \ of \ Side \ A2}{Length \ of \ Side \ B2} = …$

Example Problem: Finding Side Length

• Given two similar pentagons: JKLMN and PQRST.
• Problem: Find the length of side QR given the following relationships of side lengths:
  • QR corresponds to side RS
  • The relationships can be set up as:
  • $\frac{length \ of \ QR}{length \ of \ RS} = \frac{length \ of \ KL}{length \ of \ LM}$

Set Up the Equation

• Given values:
  • Lengths of sides are related as:
  • $ML = 5, RS = 1.5$
  • Substitute into the relationship:
  • $QR = x$
  • Based on previous data:
    • $\frac{x}{1.5} = \frac{3}{5}$

Solving for x using Cross Products

• To solve for x:
  • Cross multiplication gives:
  • $3 \cdot x = 1.5 \cdot 5$
• Simplified:
  • $3x = 7.5$
  • Then, isolate x:
  • $x = \frac{7.5}{3}$
  • $x = 2.5$

Conclusion

• Hence, the length of QR is found to be 2.5.