The perimeter of parallelogram pqsr is 74cm. what is qs?

parallelogram , opposite sides are equal

so

PR = QS

and

PQ = RS

4x - 1 = 3x + 7

x = 8

PQ = 4(8) - 1 = 32 -1 = 31

Given P = 74 cm

74 - 2(31) = 12

PR = QS = 12/2 = 6

Answer

QS = 6 cm

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

∠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.