What set of transformations are applied to parallelogram abcd to create a'b'c'd'?

question 4 (worth 4 points)

(mc 02.03)

what set of transformations are applied to parallelogram abcd to create a'b'c'd'?

parallelogram formed by ordered pairs a at negative 4, 1, b at negative 3, 2, c at negative 1, 2, d at negative 2, 1. second parallelogram transformed formed by ordered pairs a prime at 4, negative 1, b prime at 3, negative 2, c prime at 1, negative 2, d prime at 2, negative 1.

x   reflected over the x-axis and reflected over the y-axis   (correct answer)

reflected over the y-axis and rotated 180°

reflected over the x-axis and rotated 90° counterclockwise

reflected over the y-axis and rotated 90° counterclockwise

points earned on this question: 4

∠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.

answer: the answer is e

step-by-step explanation: