Corresponding angles theorem: The corresponding angles formed when a transversal crosses two or more parallel lines are congruent
The option that correctly fills the missing statements is; <u>∠CHE and ∠AGF are same side interior angles; Using addition property of equality</u>
The reason the selected option is correct is presented as follows:
The given parameters are;
AB ║ CD
Transversal EF intersects AB at G, and CD at H
The statements are written and also by using a two column proof as follows;
Given that AB and CD are parallel, and the points E, G, H, and F are collinear (on the same line)
Statement Reason
m∠EGF = 180° By definition of a straight line
∠AGE + ∠AGF = m∠EGF by Angle Addition Postulate
∠AGE + ∠AGF = 180° By substitution property
∠CHE + ∠AGF = 180° <u>∠CHE and ∠AGF are same side interior angles</u>
Same side interior angles are supplementary
∠AGE + ∠AGF = ∠CHE + ∠AGF, by substitution property of equality
m∠AGE = m∠CHE <u>Using addition property of equality</u>
m∠AGE ≅ m∠CHE By definition of congruency
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Therefore, the two missing statements are;
<u>∠CHE and ∠AGF are same side interior angles; Using addition property of equality</u>
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Learn more about the using two column proof here;
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