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Understanding Proportions and their Properties in Geometry

This guide explores the fundamentals of proportions in geometry, emphasizing properties and their applications. We discuss solving problems with proportions using the cross-product property and provide clear examples for deeper understanding. You'll find step-by-step solutions to find unknown lengths and the concept of geometric means between two numbers. With practice exercises and examples, this resource aims to enhance your problem-solving skills in geometric contexts. Gain confidence in working with proportions and learn how to apply them effectively in various problems.

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Understanding Proportions and their Properties in Geometry

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  1. Problem Solving in geom. w/ proportions

  2. Proportion Properties If then If then

  3. ExampleTrue or False If ,then If ,then true FALSE! Should be a 4!!!

  4. In the diagram Using Properties of Proportions AB AC = BD CE Find the length of BD. Do you get the fact that AB ≈ AC? Slide #4

  5. Solution AB = AC BD CE 16 = 20 x 10 20x = 160 x = 8 Given Substitute Cross Product Property Simplify So, the length of BD is 8. Slide #5

  6. Example: in the diagram,find LQ. 6 M N 13 15 LQ = 14 4 Q L P

  7. LISTEN UP! • The Geometric mean between 2 positive #’s a & b is x where • Find the geometric mean of 4 & 9. 36=x2 6=x

  8. Example: Geometric Mean between 3 and 27.

  9. Examples of Proportions A 30 16 B C 10 D E

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