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Investigation:

Similarity

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Missing, but not Gone!

Find the perimeter. SHOW YOUR WORK AND UNITS!

17.7cm

6.7cm

p

8.2cm

15.8cm

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Learning Goals

By the end of the class I will:

  • Understand the side and angle relationships between similar triangles

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Reminder

What was our definition of a “similar triangle?”

  • They have the same “shape”
  • Internal angles are all the same

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Instructions (part 1)

  • Get a piece of paper.
  • Using a ruler, measure the length of all 4 sides.
  • Mark the sides with their lengths (in cm.)
  • Draw a diagonal line across your paper.
  • Cut along the drawn line.

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Questions (Part 1)

What do you notice about these 2 triangles?

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Instructions (Part 2)

  • Set aside one of your 2 triangles.
  • On your other triangle, use a protractor and ruler to draw a line that is perpendicular to the hypotenuse that goes through the opposite vertex.
  • Cut along this line.
  • Label the vertices of each triangle with appropriate letters (Largest is ΔABC, Middle is ΔDEF, Smallest is ΔGHI.)
  • Rotate and/or flip the triangles so that the angles match (if possible)

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Questions (Part 2)

Which triangles are similar?

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Use a ruler and protractor to complete the following table:

Triangle

Hypotenuse

Short Side

Middle Side

Angles

ΔABC

​

​

​

​

ΔDEF

​

​

​

​

ΔGHI

​

​

​

​

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Calculations

Complete the calculations in the table:

Length of hypotenuse ΔDEF

Length of hypotenuse ΔABC

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Length of hypotenuse ΔDEF

Length of hypotenuse ΔGHI

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Length of shortest side ΔDEF

Length of shortest side ΔABC

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Length of shortest side ΔDEF

Length of shortest side ΔGHI

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Length of middle side ΔDEF

Length of middle side ΔABC

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Length of middle side ΔDEF

Length of middle side ΔGHI

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Questions (Part 3)

What do you notice about the ratios you calculated?

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State them as a ratios:

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These ratios are called scale factors.

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Questions (Part 4)

What conclusions can you draw from the calculated ratios?

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Are they similar or not? Why?

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Questions (Part 5)

If you were given a triangle and all 3 side lengths AND a scale factor, how could you find the lengths of the similar triangle’s sides?

​

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Two triangles are similar if they have the same shape. This means their angles are the same and their sides are proportional.