Special Right Triangles #2
Two congruent triangles can be formed by folding an equilateral triangle in half (which is the perpendicular bisector from \(\angle B\) to the base, which is also called the height) as shown in \(\triangle ABC\). One of these triangles formed is labeled \(\triangle CUP\).
- What is the length of the shortest leg \(\overline{\rm PC}\)?
- What is the length of the hypotenuse \(\overline{\rm CU}\)?
- How is the hypotenuse related to the shortest leg?
- Use the Pythagorean theorem to find the length of the longest leg \(\overline{\rm UP}\).
- How does the shortest leg relate to the longest leg?
- What is the measurement of angle \(x\)?
- What type of triangle is \(\triangle CUP\)?
- Sketch a new triangle that is similar to \(\triangle CUP\) with the shortest leg having the measurement of 2 units. Note: Similar triangles have congruent corresponding angles.
- What is the length the hypotenuse for this new triangle?
- What is the length of the longest leg for this new triangle (be sure to simplify the square root)?
- How does the length of the shortest leg compare to the hypotenuse?
- How do the lengths of the legs compare?
- Is this relationship true for any triangle that is similar to \(\triangle CUP\)
Check your solutions here.
