Fill in the missing statement and reason in the proof of the Alternate Exterior Angles Theorem. Segment AB is parallel to segment CD, and transversal EF intersects segment AB at G and segment CD at H.

It is given that segment AB is parallel to segment 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

Step-by-step explanation:

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 i.e their measures are equal

Look at the attached graph

Given:

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 (  vertical angle theorem)

∵ AB // CD and EF is a transversal

∴ m∠AGF = m∠CHF (corresponding angles theorem)

Transitive Property of Equality:  if one angle is equal to two other angles, then the two other angles are equal

 Therefore, If a = b and b = c, then a = c

∵ m∠EGB = m∠AGF

∵ m∠AGF = m∠CHF

∴ m∠EGB = m∠CHF (transitive property theorem)

 ∠EGB and ∠AGF are congruent; Transitive Property of Equality

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.