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.

A. Addition
B. Subtraction
C. Substitution
D. Transitive

CE = CD + DE and DF = EF + DE by_____.

A. Addition
B. Subtraction
C. Segment Addition
D. Transitive

CE = DF by the_____Property of Equality.

A. Addition
B. Subtraction
C. Substitution
D. Transitive

Given, AB = CE and CE = DF implies AB = DF by the____Property of Equality.

A. Addition
B. Subtraction
C. Substitution
D. Transitive

Answer 1

A. Addition

B. segment addition

C. Transitive

D. Transitive

Explanation:

CD + DE = EF + DE by the Addition Property of Equality.

CE = CD + DE and DF = EF + DE by segment addition

CE = DF by the Transitive Property of Equality.

Given, AB = CE and CE = DF implies AB = DF by the Transitive Property of Equality.

Correct for plato, I just took the test ;)

Answer 2

In the figure, CD = EF and AB = CE

To prove that AB = DF:

Step 1:

Given CD = EF, so we can substitute EF instead of CD.

CD + DE = EF + DE

by the Substitution Property of Equality.

Here, Option C is the correct answer.

Step 2:

CD + DE = CE and

EF + DE = DF

by Segment Addition.

Here, Option C is the correct answer.

Step 3:

From step 1, CD + DE = EF + DE

From step 2, CE = DF

So, CE = DF by the Transitive Property of Equality.

Here, Option D is the correct answer.

Step 4:

Given AB = CE and CE = DF

⇒ AB = DF

by the Transitive Property of Equality.

Here, Option D is the correct answer.

Hence proved.