Wrap-Up


Lesson Summary

In this lesson, we learned the following:

  • Two triangles are similar when they satisfy any of the following rules:
    • Angle-angle similarity (two equal angles)
    • Side-angle-side similarity (two sides in the same proportion and the contained angle is equal)
    • Side-side-side similarity (all three sides are in the same proportion)
    Angle-Angle (AA) Side-Angle-Side (SAS) Side-Side-Side (SSS)
    Triangle with 3 angles labelled. Triangle with 1 angle labelled between two sides with lengths 10 and 8. Triangle with side lengths 10, 8, and 15.
    Larger triangle with the same 3 angles. Triangle with same size angle labelled between two sides with lengths 15 and 12. Triangle with side lengths 15,12, and 22.5.
  • Similar triangles can be constructed to solve for unknown distances in real-world problems.

Take It With You

The first calculation of the circumference of the Earth was performed by Eratosthenes around \(240\) BCE based on the following observation.

If the Sun is directly overhead in the city of Syene, then at the same time in the city of Alexandria (\(850\) km away) a pole would have to be tilted roughly \(7\) degrees away from vertical (towards the Sun) to not cast a shadow.

Can you use this information to estimate the circumference of the Earth?