Question

Fill in the missing statement and reason in the proof of the corresponding angles theorem.

Answer 1

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; ∠CHE and ∠AGF are same side interior angles; Using addition property of equality

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°    ${}$        ∠CHE and ∠AGF are same side interior angles

Same side interior angles are supplementary

∠AGE + ∠AGF = ∠CHE + ∠AGF, by substitution property of equality

m∠AGE = m∠CHE      ${}$           Using addition property of equality

m∠AGE ≅ m∠CHE     ${}$           By definition of congruency

Therefore, the two missing statements are;

∠CHE and ∠AGF are same side interior angles; Using addition property of equality

Learn more about the using two column proof here;

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