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EXAMPLE 4

You are designing a logo to sell daffodils. Use the information given. Determine whether m EBA = m DBC . Equation. Explanation. Reason. m ∠ 1 = m ∠ 3. m EBA = m 3+ m 2. m EBA = m 1+ m 2. Substitute m 1 for m 3 . EXAMPLE 4. Use properties of equality.

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EXAMPLE 4

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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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