# Making Scale Drawings Using the Parallel Method

### New York State Common Core Math Geometry, Module 2, Lesson 3

Student Outcomes

• Students create scale drawings of polygonal figures by the Parallel Method.
• Students explain why angles are preserved in scale drawings created by the Parallel Method using the theorem on parallel lines cut by a transversal.

Making Scale Drawings Using the Parallel Method

Classwork

Opening Exercise

Dani dilated β³ π΄π΅πΆ from center π, resulting in β³ π΄β²π΅β²πΆβ². She says that she completed the drawing using parallel lines. How could she have done this? Explain.

Example 1

a. Use a ruler and setsquare to draw a line through πΆ parallel to π΄π΅. What ensures that the line drawn is parallel to π΄π΅?
b. Use a ruler and setsquare to draw a parallelogram π΄π΅πΆπ· around π΄π΅ and point οΏ½

Example 1

1. Create a scale drawing of the figure below using the ratio method about center π and scale factor π = 3/4. Verify that the resulting figure is in fact a scale drawing by showing that corresponding side lengths are in constant proportion and the corresponding angles are equal in measurement.

Example 2

Use the figure below with center π and a scale factor of π = 2 and the following steps to create a scale drawing using the parallel method.

Step 1. Draw a ray beginning at π through each vertex of the figure.
Step 2. Select one vertex of the scale drawing to locate; we have selected π΄β². Locate π΄β² on ππ΄ so that ππ΄ β² = 2ππ΄.
Step 3. Align the setsquare and ruler as in the image below; one leg of the setsquare should line up with side π΄π΅, and the perpendicular leg should be flush against the ruler.
Step 4. Slide the setsquare along the ruler until the edge of the setsquare passes through π΄β². Then, along the perpendicular leg of the setsquare, draw the segment through π΄β² that is parallel toπ΄π΅ until it intersects with ππ΅, and label this point π΅β².
Step 5. Continue to create parallel segments to determine each successive vertex point. In this particular case, the setsquare has been aligned with π΄πΆ. This is done because, in trying to create a parallel segment from π΅πΆ, the parallel segment was not reaching π΅β². This could be remedied with a larger setsquare and longer ruler, but it is easily avoided by working on the segment parallel to π΄πΆ instead.
Step 6. Use your ruler to join the final two unconnected vertices.

Exercises

1. With a ruler and setsquare, use the parallel method to create a scale drawing of ππππ by the parallel method. πβ² has already been located for you. Determine the scale factor of the scale drawing. Verify that the resulting figure is in fact a scale drawing by showing that corresponding side lengths are in constant proportion and that corresponding angles are equal in measurement.
2. With a ruler and setsquare, use the parallel method to create a scale drawing of π·πΈπΉπΊ about center π with scale factor π = 1/2. Verify that the resulting figure is in fact a scale drawing by showing that corresponding side lengths are in constant proportion and that the corresponding angles are equal in measurement.
3. With a ruler and setsquare, use the parallel method to create a scale drawing of pentagon πππππ about center π with scale factor 5/2. Verify that the resulting figure is in fact a scale drawing by showing that corresponding side lengths are in constant proportion and that corresponding angles are equal in measurement.

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