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