For numbers 6-10, U is the midpoint of line segment AE. CU is congruent to TU. Prove that triangle AAUC' is similar to triangle ATUE.
Statements:
1. U is the midpoint of line segment AE.
2. Definition of a midpoint.
3. CU is congruent to TU.
4. Given.
5. AAUC' is a triangle.
6. ATUE is a triangle.
7. Definition of a triangle.
8. AAUC' has angle AUC equal to angle ATU.
9. AAUC' has angle AAU equal to angle ATU.
10. AAUC' has angle AUC' equal to angle ATU.
11. AAUC' is similar to ATUE.
Reasons:
1. Given.
2. Definition of a midpoint.
3. Given.
4. Given.
5. Definition of a triangle.
6. Definition of a triangle.
7. Definition of a triangle.
8. Corresponding angles of similar triangles are congruent.
9. Corresponding angles of similar triangles are congruent.
10. Corresponding angles of similar triangles are congruent.
11. If two triangles have three pairs of corresponding angles that are congruent, then the triangles are similar.