Question

Select the correct answer from each drop-down menu. In the figure, CD = EF and AB = CE. Complete the statements to prove that AB = DF. CD + DE = EF + DE by the Property of Equality. CE = CD + DE and DF = EF + DE by . CE = DF by the Property of Equality. Given, AB = CE and CE = DF implies AB = DF by the Property of Equality.

Answer 1

The correct statement :

CE=DF

Transitive Property of Equality                  

Further explanation

Equality means having the same value.

Usually stated with the symbol "="

It says inequality if there are symbol forms like <,>, ≤ or ≥

There are several PROPERTIES OF EQUALITY

•  Addition Property of Equality If a = b, then a + c = b + c.

•  Subtraction Property of Equality If a = b, then a - c = b - c.

• Multiplication Property of Equality If a = b, then a x c = b x c.

•  Division Property of Equality If a = b, then a / c = b / c.

Given, AB = CE and CD = DF

Prove: AB = DF

• Step 1

CD = EF

Addition Property of Equality (we add DE on both sides)

CD + DE = DE + EF ... equation 1

• Step 2

From the lines in the picture:

CE = CD + DE

DF = DE + EF

So from equation 1:

CE = DF .... equation 2

• Step 3

From Given AB = CE, then equation 2 becomes:

AB = DF ----> Proven

Learn more

Algebraic expressions

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Keywords : Property of Equality, prove, line

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