Question

Given that RT ≅ WX, which statement must be true?

Answer 1

RT + TW = WX + TW must be true.

Answer 2

Since RT ≅ WX, RT and WX are congruent; in other words they are completely equal for all purposes. Given that, we can substitute RT with WX in the equations and solve them to check which one is valid. The valid equation will be to true statement.

For RT + TW = WX + TW

Step 1 replace RT with WX

RT + TW = WX + TW

WX + TW = WX + TW

Step 2 subtract TW from both sides of the equation

WX + TW - TW= WX + TW -TW

WX = WX

Since RT ≅ WX, the equation WX = WX is valid because, as we stated before, RT and WX are completely equal, and thus, interchangeable.

We can conclude that the correct statement is: RT + TW = WX + TW

Since we already found the valid statement, we don't need to check the other ones, but lets do it just for fun:

For RT = 2(RX) and WX = 2(RX)

Step 1 replace RT with WX:

WX = 2(RX)

Since we don't know anything about RX, we can't conclude that RT = WX from the given statement. Therefore, we can't conclude that the statement must be true.

For RT + TW = RX

Step 1 replace RT with WX:

WX + TW = RX

Step 2 subtract TW from both sides:

WX + TW - TW = RX - TW

WX = RX - TW

Again, since we don't know anything about RX and TW, we can conclude that RT = WX from the given statement. . Therefore, we can't conclude that the statement must be true.