Questions: ABCD is a rectangle with some right triangles inside it. Redraw the triangles, so they are oriented the same way to make it easier. Don't use vertex B or C. I. List at least two triangles that are similar to Triangle AED?

Solution Steps

We are looking for triangles similar to triangle AED. Similar triangles have corresponding angles that are congruent. Triangle AED has a right angle at F, and angle EAD is congruent to angle EDA.

Triangle EFD is similar to AED. Both have a right angle, and they share angle EDA. Therefore, their third angles must also be congruent. Thus, triangle AED ~ triangle EFD.

Triangle AFE is similar to AED. Both have a right angle. Angle EAF in triangle AFE is congruent to angle EDA in triangle AED. They are alternate interior angles since lines BC and AD are parallel, and AE is a transversal. Therefore, their third angles must also be congruent. Thus, triangle AED ~ triangle AFE.

Final Answer