It is given that ab is parallel to cd and points e, g, h, and f are collinear. by the vertical angles theorem. ∠agf and ∠chf are corresponding and congruent according to the corresponding angles theorem. finally, ∠egb and ∠chf are congruent by the
∠egb and ∠ega are congruent; transitive property of equality
∠egb and ∠agf are congruent; transitive property of equality
∠egb and ∠agf are congruent; subtraction property
∠egb and ∠ega are congruent; subtraction property

∠EGB and ∠AGF are congruent;

Transitive Property of Equality ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The vertical angles theorem is about the angles that are

 opposite to each other

- These angles are formed when two lines cross each other

- Vertical angles are congruent means their measures are equal

- Look to attached graph

- AB // CD

- E , G , H , F are col-linear

- The line which contains points E , G , H , F is a transversal for the

 parallel lines AB and CD

∵ AB and EF intersected at point G

∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem

- When lines AB and EF intersected at G they formed opposite

 angles like angles EGB and AGF, then angles EGB and AGF are

 congruent according to the vertical angle theorem

∵ AB // CD and EF is a transversal

∴ m∠AGF = m∠CHF ⇒ by corresponding angles theorem

- Transitive Property of Equality means if one angle is equal to two

 other angles, then the two other angles are equal

  If a = b and b = c, then a = c

* Lets use it

∵ m∠EGB = m∠AGF

∵ m∠AGF = m∠CHF

∴ m∠EGB = m∠CHF ⇒ by transitive property theorem

* The answer is:

 ∠EGB and ∠AGF are congruent;

  Transitive Property of Equality

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step-by-step explanation:

the answer is a