Question

Instructions: Complete the following proof by dragging and dropping the correct reason into the space

provided.
Given: RS= XY, ST = WX
Prove: RT = WY

Answer 1

Proof:

Given: RS = XY and ST = WX

To prove: RT = WY

We'll start by using the Transitive Property of Equality. If two segments are equal to the same segment, then they are equal to each other.

RS = XY (Given)

XY = WY (Substitution, since RS = XY)

RS = WY (Transitive Property of Equality, combining statements 1 and 2)

Now, we'll use the Segment Addition Postulate. According to the postulate, if three points A, B, and C are collinear, then AB + BC = AC.

RT = RS + ST (Segment Addition Postulate)

RT = WY + ST (Substitution, using statement 3)

RT = WY + WX (Substitution, since ST = WX)

Using the Associative Property of Addition, which states that the grouping of numbers being added does not affect the sum, we can rearrange the terms in statement 6.

RT = WX + WY (Associative Property of Addition)

Finally, using the Commutative Property of Addition, which states that the order of numbers being added does not affect the sum, we can reorder the terms in statement 7.

RT = WY + WX (Commutative Property of Addition)

From statement 8, we can see that RT = WY, which proves the given statement.

Therefore, RT = WY.