Now consider the expression x2 + 6x + 7. The pieces of this
expression can be represented with an "x by x" square, six "x by 1"
rectangles, and seven unit squares.
x2 + 6x + 7
a. Why is it impossible to arrange the given squares and rectangles
without overlapping to form one large square?
b. How could you produce the requested square if you were given
some extra pieces or allowed to take away some pieces? What
addition or subtraction would do the job most efficiently?
c. Explain how your answer to Part b illustrates the fact that
x2 + 6x + 7 = (x + 3)2 – 2.

answer: the answer is 35%

∠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.

step-by-step explanation: