Question

Consider triangle XYZ with altitude to the hypotenuse ZW .

Given: Right triangle XYZ with an altitude ZW
a. Describe a sequence of transformations that maps triangle XYZ to triangle XZW
b. Describe a sequence of transformations that maps triangle XYZ to triangle ZYW.

Answer 1

To map triangle XYZ to triangle XZW, first reflect triangle XYZ across the altitude line ZW, then rotate it counterclockwise by 90 degrees around point X. To map triangle XYZ to triangle ZYW, first reflect triangle XYZ across the altitude line ZW, then rotate it clockwise by 90 degrees around point Z.

Step-by-step explanation:

To map triangle XYZ to triangle XZW, the following sequence of transformations can be used:

1. Reflect triangle XYZ across the altitude line ZW to obtain triangle XZY.
2. Rotate triangle XZY by 90 degrees counterclockwise around point X to obtain triangle XZW.

To map triangle XYZ to triangle ZYW, the following sequence of transformations can be used:

1. Reflect triangle XYZ across the altitude line ZW to obtain triangle XZY.
2. Rotate triangle XZY by 90 degrees clockwise around point Z to obtain triangle ZYW.