## 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 2â€“4 (9 minutes)
Students complete Exercises 2â€“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) âƒ—. 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 5â€“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 âˆ 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 âˆ XYZ? How do you know?
The measure is 38Â°. 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 $$\overrightarrow{E F}$$?
$$\overleftrightarrow{\boldsymbol{B B}^{\prime}} \| \overleftrightarrow{\boldsymbol{E F}}$$

Question 4.
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 $$\overleftrightarrow{\boldsymbol{H}^{\prime} \boldsymbol{I}^{\prime}}$$||$$\overleftrightarrow{\boldsymbol{J}^{\prime} \boldsymbol{K}^{\prime}}$$.