Question

Match the following items. Given rstu is a parallelogram, which of the following statements are true?

1) ws = st
2) rw = uw
3) ru = wt
4) ut = rs

Answer 1

In a parallelogram RSTU, only the statement that UT equals RS can be confirmed as true, because opposite sides in a parallelogram are equal. The other statements refer to points or lines not defined in the context of parallelogram RSTU.

Step-by-step explanation:

When discussing a parallelogram such as RSTU, there are specific properties that can help us determine if the given statements are true. Let's explore these statements one by one:

• 1) WS = ST: This statement cannot be determined as true or false because WS and ST are not described within the parallelogram RSTU. This seems to be irrelevant to the parallelogram properties.
• 2) RW = UW: Similar to the first statement, RW and UW are not part of the described parallelogram RSTU and thus cannot be evaluated within this context.
• 3) RU = WT: Again, since WT is not a side of parallelogram RSTU, we cannot determine if this statement is true without additional information.
• 4) UT = RS: In a parallelogram, opposite sides are equal in length. Therefore, side UT is equal in length to side RS, making this statement true.

It's important while evaluating statements about geometric figures to rely on the defined properties and characteristics of those figures. In this case, only the last statement about the sides of the parallelogram RSTU can be confirmed as true based on the properties of parallelograms.