GEOM 2 | Lesson 3 | Try This! (Special Right Triangles #1)

Special Right Triangles #1

Two congruent triangles can be formed by folding a square with sides = 1 unit on either of its diagonals as shown in \(\square ABCD\).  One of those triangles formed is labeled \(\triangle PAN\).

  1. What are the lengths of the legs of \(\triangle PAN\)?
  2. Use the Pythagorean theorem to find the length of the hypotenuse \(\overline{\rm PN}\).
  3. What are the measurements of angles \(x\) and \(y\)?
  4. What type of triangle is \(\triangle PAN\)?
  5. Sketch a new triangle that is similar to \(\triangle PAN\) with legs that measure 2 units each.  Note: Similar triangles have congruent corresponding angles.
  6. What is the length the hypotenuse for this new triangle (be sure to simplify the square root) ?
  7. How do the lengths of the legs compare to the length of the hypotenuse?
  8. Is this relationship true for any triangle that is similar to \(\triangle PAN\)?

Check your solutions here.

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