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Fill in the blink

Given ,Simplify ,BC=EF ,Multiplication Property of Equality ,Substitution Property of Equality AC=DF DE+EF=DF Reflexive Property of Equality Transitive Property of Equality ,Segment Addition Postulate, Division Property of Equality ,Addition Property of Equality, Distributive Property, Subtraction Property of Equality

Fill in the blink Given ,Simplify ,BC=EF ,Multiplication Property of Equality ,Substitution-example-1

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Answer:

see below

Explanation:


\displaystyle AB = DE

[given]


\displaystyle \boxed{BC = EF}

[given]


\displaystyle AB + BC = AC

[segment addition Postulate]


\displaystyle \boxed{DE+ EF=DF}

[segment addition Postulate]


\rm\displaystyle DE+ BC = AC \: \: \text{and} \: \: DE+ BC = DF

[Substitution Property of Equality]


\displaystyle \boxed{AE= DE}

[Proven]

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