34. The sum of the lengths of the two bases of a trapezoid

is 22 cm, and its area is 66 cm". What is the height of

the trapezoid?

h=6

Step-by-step explanation:

the formula for a trapezoid’s area is to multiply the bases (a and b) by the height of the trapezoid, then divide it all by 2.

so typed out, that would look like:

((a+b) h) / 2

and in the case of this problem:

((22) h) / 2 = 66

so just go ahead and solve it algebraically from there and you’re good!

∠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.