In this section, you will use dilations in order to generate similar figures.

Interactive exercise. Assistance may be required. Use the interactive below to dilate ΔABC. Click and drag on the slider to dilate ΔABC to create ΔDEF. The number on the slider indicates the scale factor used to generate the dilation. Use the interactive to complete the table that follows. Use the table to answer the questions after the table.

Generating Similar Figures from Dilations

Use the slider to dilate ΔABC by the scale factor indicated on the slider.

(c) OnTRACK for College Readiness

6 May 2014, Created with GeoGebra


Copy and paste the table below to your notes, or a word processing document, to enter your data.

Scale Factor (f)
DE over AB DE AB
BC over EF EF BC
DF over AC DF AC
0.25
      
0.75
      
2
      
2.5
      

Interactive popup. Assistance may be required.

Check Your Answer

Scale Factor (f)
DE over AB DE AB
BC over EF EF BC
DF over AC DF AC
0.25
0.25
0.25
0.25
0.75
0.75
0.75
0.75
2
2
2
2
2.5
2.5
2.5
2.5
Close Pop Up

Pause and Reflect

In the interactive, you used a dilation to generate a pair of similar triangles. Do you think the same relationship would hold true if you dilated a quadrilateral? Why or why not?

Interactive popup. Assistance may be required.

Check Your Answer

Yes. A dilation multiplies the length of each side of an original quadrilateral by the same scale factor. When you calculate the ratios of the lengths of the corresponding sides, it will always be equal to the scale factor used to generate the dilation. Since the ratios are equal, the lengths of the sides are proportional.Close Pop Up

Practice

  1. In the figure below, Δ JKL is generated by dilating Δ DEF by a scale factor of 1.8.

    Write an expression that could be used to calculate JL.

    Interactive popup. Assistance may be required.

    Need a hint?

    What side of Δ DEF corresponds with JL?Close Pop Up
    Interactive popup. Assistance may be required.

    Check Your Answer

    JL = 6.3 × 1.8Close Pop Up
  2. In the diagram below, parallelogram WXYZ is generated by dilating parallelogram BCDE by a factor of 40%.

    Which side of parallelogram WXYZ corresponds with DE?

    Interactive popup. Assistance may be required.

    Need a hint?

    DE lies between angle D and angle E in parallelogram BCDE. Which two angles are in the same position of parallelogram WXYZ? Close Pop Up
    Interactive popup. Assistance may be required.

    Check Your Answer

    YZ corresponds with DE.Close Pop Up
  3. In the figure below, points A, D, F, and H lie on line a. Triangles AFE and AHG are dilations of ΔADC.

    In ΔAFE, which side corresponds with AC from ΔADC?

    Interactive popup. Assistance may be required.

    Need a hint?

    How are ΔAFE and ΔADC related in terms of their orientations? Close Pop Up
    Interactive popup. Assistance may be required.

    Check Your Answer

    AE corresponds with AC. Close Pop Up