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Multiplication and Division Properties in Geometry

Discover Theorems 14 and 15 - how congruent segments/angles have congruent multiples and divisions. Learn when to apply these properties and keywords like midpoint and trisect. Explore HOCSAC and HOCAAC extensions for halving congruent segments/angles. Practice proofs with addition, subtraction, multiplication, and division properties.

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Multiplication and Division Properties in Geometry

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  1. Section 2.6 Multiplication and Division Properties

  2. Theorem 14: If segments (or angles) are congruent, their like multiples are congruent. (Multiplication Property) Theorem 15: If segments (or angles) are congruent, their like divisions are congruent. (Division Property)

  3. Using the Multiplication and Division Properties • A multiplication property is used when the segments or angles in the conclusion are greater than those in the given information • A division property is used when the segments or angles in the conclusion are smaller than those in the given information. • Watch for keywords…midpoint…trisect …

  4. HOCSAC & HOCAAC Two Extensions of the Division Property HOCSAC: Halves of Congruent Segments are Congruent HOCAAC: Halves of Congruent Angles are Congruent

  5. Proof Practice Using: Addition, Subtraction, Multiplication, Division Properties

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