Fill in the missing statement and reason in the proof of the Alternate Interior 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. ∠AGF and ∠EGB are vertical and congruent by the Vertical Angles Theorem. ∠EGB and ∠EHD are congruent according to the . Finally, by the Transitive Property of Equality.

Corresponding Angles Theorem; ∠AGF and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠EGB and ∠EHD are congruent
Corresponding Angles Theorem; ∠EGB and ∠EHD are congruent
Alternate Exterior Angles Theorem; ∠AGF and ∠EHD are congruent

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see attached graph

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

their is no graph showing

step-by-step explanation: