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Logo Design for Daffodil Sales Incorporating Angle Properties and Equality Concepts

This project focuses on designing a logo to promote daffodil sales while incorporating mathematical concepts related to angle properties and equality. We demonstrate how properties such as the Angle Addition Postulate, Transitive Property, and properties of equality can be creatively integrated into the design. The logo will effectively symbolize the beauty of daffodils alongside the precision and balance found in geometric principles, reinforcing the connection between nature and mathematics.

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Logo Design for Daffodil Sales Incorporating Angle Properties and Equality Concepts

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  1. You are designing a logo to sell daffodils. Use the information given. Determine whether mEBA=mDBC. Equation Explanation Reason m∠ 1 = m∠ 3 mEBA =m 3+ m 2 mEBA =m 1+ m 2 Substitute m1 for m3. EXAMPLE 4 Use properties of equality LOGO SOLUTION Marked in diagram. Given Add measures of adjacent angles. Angle Addition Postulate Substitution Property of Equality

  2. m 1 + m 2 = mDBC mEBA = mDBC Both measures are equal to the sum of m1 +m2. EXAMPLE 4 Use properties of equality Add measures of adjacent angles. Angle Addition Postulate Transitive Property of Equality

  3. In the diagram, AB = CD. Show that AC = BD. Equation Explanation Reason EXAMPLE 5 Use properties of equality SOLUTION Marked in diagram. AB = CD Given AC = AB + BC Add lengths of adjacent segments. Segment Addition Postulate BD = BC + CD Add lengths of adjacent segments. Segment Addition Postulate

  4. EXAMPLE 5 Use properties of equality Add BCto each side of AB = CD. AB + BC = CD + BC Addition Property of Equality AC = BD Substitute ACfor AB + BCand BDfor BC +CD. Substitution Property of Equality

  5. 4. If m 6 = m 7, then m 7 = m 6. ANSWER Symmetric Property of Equality ANSWER Transitive Property of Equality for Examples 4 and 5 GUIDED PRACTICE Name the property of equality the statement illustrates. 5. If JK = KLand KL = 12, then JK = 12.

  6. 6. m W = m W ANSWER Reflexive Property of Equality for Examples 4 and 5 GUIDED PRACTICE

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