Given trapezoid PQRS, find the length of midsegment TU.

Option (4)

Step-by-step explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) =

7x - 26 =

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

          = 7(36) - 26

          = 252 - 26

          = 226

Therefore, Option (4) will be the answer.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

idk

step-by-step explanation: