Question

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

Answer 1

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]