Use the image to answer the question.Given: Isosceles trapezoid EFGH with EF¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯ Prove: Opposite angles ∠EFG and ∠EHG are supplementary.When naming angles, put the letters in alphabetical order as much as possible.StatementsReasons1. Isosceles trapezoid EFGH with EF¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯ .1. __________2. ∠EHG≅∠FEH 2. __________3. ___________3. Same side interior angles are supplementary.4. m∠EHG+∠FGH=180° 4. ___________5. ∠EFG+∠EHG=180° 5. Substitution Property6. __________6. definition of supplementary angles

Answer 1

Here is the completed proof with the missing statements and reasons filled in:

Statements | Reasons --- | ---

1. Isosceles trapezoid EFGH with \( EF \cong GH \) | 1. Given
2. \( \angle EHG \cong \angle FEH \) | 2. Base angles of isosceles trapezoid are congruent
3. \( m\angle EHG + m\angle FGH = 180^\circ \) | 3. Same side interior angles are supplementary
4. \( m\angle EHG + m\angle FGH = 180^\circ \) | 4. As stated in step 3
5. \( m\angle EFG + m\angle EHG = 180^\circ \) | 5. Substitution Property
6. \( \angle EFG \) and \( \angle EHG \) are supplementary. | 6. Definition of supplementary angles

By filling in the missing statements and reasons, we successfully prove that the opposite angles \( \angle EFG \) and \( \angle EHG \) are supplementary.