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.

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08-08-2019
Mathematics

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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.

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indrawboy indrawboy · Answer 1 · 2019-11-22T08:47:10+01:00

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

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ashdestiny5 ashdestiny5 · Answer 2 · 2020-12-17T05:26:03+01:00

1. Addition Property of Equality

2. Segment addition

3. Substitution Property of Equality.

4. Transitive Property of Equality.

Step-by-step explanation:

Here, given : CD = EF and AB = CE

To Show: AB = DF

Now, as given in the steps:

1. CD + DE = EF + DE by the (addition) Property of Equality.

As we have added the EQUAL QUANTITY on both sides of the equality.

2.CE = CD + DE and DF = EF + DE by (segment addition).

As here CE and DF are line segments. And the length of a

Line Segment = Sum of all its parts in which it is divided.

3.CE = DF by the (Addition, subtraction, substitution, transitive)Property of Equality.

Here, as we know CE = CD + DE

but CD = EF , so SUBSTITUTE EF in place of CD

⇒ CE = EF + ED = FD (by substitution) Property of Equality.

4.Given, AB = CE and CE = DF implies AB = DF by the (transitive)Property of Equality.

As, x = y , y = z ⇒ x = z is the TRANSITIVE PROPERTY