Given: AEFH and AGFH are right triangles.
Prove: AFHAAGFH is a right triangle.
Statements Reasons
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1. AEFH and AGFH are right triangles. Given
2. ∠ZFHE and ∠LEHG are right angles. Definition of right triangles
3. ∠LRHE = ∠AERH and ∠ZFKG = ∠AGFH All right angles are congruent (given)
4. ∠FHA = ∠FK and ∠ABFH = ∠AOFK Definition of isosceles triangles
5. ZEFH < ZGFH Given
6. EH = GH Symmetric property
7. ∠ZFHO = ∠EF = ∠GF Transitive property
8. ∠LL Theorem HL Theorem
9. ZFaZK = EH = GH Definition of congruent angles
10. ZF = GF Transitive property
11. ∠Dall~ilc Drars Definition of congruent angles
Therefore, AFHAAGFH is a right triangle.