## Engage NY Eureka Math 8th Grade Module 2 End of Module Assessment Answer Key

### Eureka Math Grade 8 Module 2 End of Module Assessment Task Answer Key

Question 1.

△ABC≅ △A’B’C’. Use the picture to answer the question below.

Describe a sequence of rigid motions that would prove a congruence between △ABC and △A’B’C’.

Answer:

Let T be the Translation AWNG \(\overrightarrow{A^{\prime} A}\) so that t(A’) = A. Let R be the rotation around A, d degrees so that R(A’B’) = AB. By hypothesis |AB| = |A’B’|. Let |∠A| = |∠A|, |∠B| = |∠B|, so the composition ʌ.R.T will map ∆A’B’C’ to ∆A’B’C’ to ∆ABC, i.e., ʌ(R(T(△A’B’C’))) = △ABC

Question 2.

Use the diagram to answer the question below.

k || l

Answer:

Line k is parallel to line l. m∠EDC=41° and m∠ABC=32°. Find the m∠BCD. Explain in detail how you know you are correct. Add additional lines and points as needed for your explanation.

Answer:

Let F be a point on line or so that ∠DCF is a straight angle. Then because r || l, ∠EDC ≅ ∠CFA and have equal measure. ∠ABC and ∠CFA are the remote interior angles of △BCF which means ∠BCD = ∠ABC + CFA. Therefore ∠BCD = 32 + 41 = 73°.

Question 3.

Use the diagram below to answer the questions that follow. Lines L_{1} and L_{2} are parallel, L_{1} || L_{2}. Point N is the midpoint of segment GH.

a. If the measure of ∠IHM is 125°, what is the measure of ∠IHJ? ∠JHN? ∠NHM?

Answer:

∠IHJ = 55°

∠JHN = 125°

∠NHM = 55°

b. What can you say about the relationship between ∠4 and ∠6? Explain using a basic rigid motion. Name another pair of angles with this same relationship.

Answer:

∠4 & ∠6 are alternate interior angles that are equal because L_{1} || L_{2}. Let R be a rotation of 180° around point N. Then R(N) = N, R(L_{3}) = L_{3} and R(L_{1}) = L_{2}. Rotations are degree preserving so (∠4) = ∠6

∠3 & ∠5 are also alternate interior angles that are equal.

c. What can you say about the relationship between ∠1 and ∠5? Explain using a basic rigid motion. Name another pair of angles with this same relationship.

Answer:

∠1 & ∠5 are corresponding angles that are equal because L_{1} || L_{2}. Let T be the Translation along vector \(\overrightarrow{G H}\). Then T(L_{2}) = L_{1} and T(∠5) = ∠1.

∠3 & ∠7 are also corresponding angles that are equal.