## Engage NY Eureka Math 8th Grade Module 2 Lesson 3 Answer Key

### Eureka Math Grade 8 Module 2 Lesson 3 Exercise Answer Key

Exercise 1.
Draw a line passing through point P that is parallel to line L. Draw a second line passing through point P that is parallel to line L and that is distinct (i.e., different) from the first one. What do you notice?  Students should realize that they can only draw one line through point P that is parallel to L.

Exercises 2–4 (9 minutes)
Students complete Exercises 2–4 independently in preparation for the discussion that follows.

Exercise 2.
Translate line L along the vector $$\overrightarrow{A B}$$. What do you notice about L and its image, L’?  L and L’ coincide. L=L’.

Exercise 3.
Line L is parallel to vector $$\overrightarrow{A B}$$. Translate line L along vector (AB) ⃗. What do you notice about L and its image, L’?  L and L’ coincide, again. L=L’.

Exercise 4.
Translate line L along the vector $$\overrightarrow{A B}$$. What do you notice about L and its image, L’?  L || L’

Exercises 5–6 (5 minutes)
Students complete Exercises 5 and 6 in pairs or small groups.

Exercise 5.
Line L has been translated along vector $$\overrightarrow{A B}$$, resulting in L’. What do you know about lines L and L’? L || T(L)

Question 6.
Translate L1 and L2 along vector $$\overrightarrow{D E}$$. Label the images of the lines. If lines L1 and L2 are parallel, what do you know about their translated images?  Since L1 || L1, then (L1)’ || (L2)’.

### Eureka Math Grade 8 Module 2 Lesson 3 Exit Ticket Answer Key

Question 1.
Translate point Z along vector $$\overrightarrow{A B}$$. What do you know about the line containing vector $$\overrightarrow{A B}$$ and the line formed when you connect Z to its image Z’? The line containing vector $$\overrightarrow{A B}$$ and ZZ’ is parallel.

Question 2.
Using the above diagram, what do you know about the lengths of segment ZZ’ and segment AB?
The lengths are equal: |ZZ’|=|AB|.

Question 3.
Let points A and B be on line L and the vector $$\overrightarrow{A C}$$ be given, as shown below. Translate line L along vector $$\overrightarrow{A C}$$. What do you know about line L and its image, L’? How many other lines can you draw through point C that have the same relationship as L and L’? How do you know?  L and L’ are parallel. There is only one line parallel to line L that goes through point C. The fact that there is only one line through a point parallel to a given line guarantees it.

### Eureka Math Grade 8 Module 2 Lesson 3 Problem Set Answer Key

Question 1.
Translate ∠XYZ, point A, point B, and rectangle HIJK along vector $$\overrightarrow{E F}$$. Sketch the images, and label all points using prime notation.  Question 2.
What is the measure of the translated image of ∠XYZ? How do you know?
The measure is 38°. Translations preserve angle measure.

Question 3.
Connect B to B’. What do you know about the line that contains the segment formed by BB’ and the line containing the vector $$\overrightarrow{E F}$$?
$$\overleftrightarrow{\boldsymbol{B B}^{\prime}} \| \overleftrightarrow{\boldsymbol{E F}}$$
Connect A to A’. What do you know about the line that contains the segment formed by AA’ and the line containing the vector $$\overrightarrow{\boldsymbol{E F}}$$?
$$\overleftrightarrow{A A^{\prime}}$$ and $$\overleftrightarrow{\boldsymbol{E F}}$$ coincide.
Since HIJK is a rectangle, I know that $$\overleftrightarrow{\boldsymbol{H} \boldsymbol{I}}$$ || $$\overleftrightarrow{\boldsymbol{J K}}$$. Since translations map parallel lines to parallel lines, then $$\overleftrightarrow{\boldsymbol{H}^{\prime} \boldsymbol{I}^{\prime}}$$||$$\overleftrightarrow{\boldsymbol{J}^{\prime} \boldsymbol{K}^{\prime}}$$.