EXAMPLE 4 Use properties of equality LOGO You are designing a logo to sell daffodils. Use the information given. Determine whether m EBA = m DBC. SOLUTION.

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Presentation transcript:

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

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

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

EXAMPLE 5 Use properties of equality AB + BC = CD + BC Add BC to each side of AB = CD. Addition Property of Equality AC = BD Substitute AC for AB + BC and BD for BC + CD. Substitution Property of Equality

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

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