Part A Now, determine whether the relationship between the two triangles you found in the first task is true for any two triangles. For any line, if you draw two right triangles using the line as the hypotenuse, can the triangles be congruent? Why or why not? Do they have to be congruent? Why or why not?

Part B
For any line, if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?

Part C
For similar triangles, the side lengths are proportional. So, you can write a proportion relating the two pairs of vertical and horizontal side lengths. For the line y = 2x, a triangle can be drawn 2 units up and 1 unit right from the origin.

Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.

Part D
If the vertical length is 10 , what is the horizontal length?

Part E
Using the slope program, create the line y = 2x. Keeping the line the same, move one (or both) of the points so the triangle created by the points has a vertical length of 10 units. What is the horizontal length? Does this horizontal length match the answer you found in the previous question?

Part F
Solve the equation from Part C so that y is by itself on one side of the equation. How are this equation and the equation of the line related? What does this relationship mean about any triangle created using this line?