Question

Fill in the missing statement and reason in the proof of the Alternate Exterior Angles

Answer 1

The addition property of equality states that if you add the same value to both sides of an equation, the sides of the equation stay equal

∠EGB  and ∠AGF are congruent by addition property

Reason:

AB is parallel to CD;    Given

Points E, G, H, and F are collinear;    Given

The measure of ∠EGF = 180° by angles on a straight line

∠AGF and ∠AGE are adjacent angles, therefore, ∠AGF + ∠AGE = ∠EGF

• ∴ ∠AGF + ∠AGE = 180° by transitive property

∠CHE and ∠AGF are same side interior angles

• ∴ ∠CHE + ∠AGF = 180°

∠AGF + ∠AGE = ∠CHE + ∠AGF

Therefore, the measure of ∠AGE is equal to the measure of ∠CHE by addition property of equality

• ∠EGB + ∠AGE = ∠AGF + ∠AGE by linear pair angles

Therefore;

∠EGB  and ∠AGF are congruent by the addition property of equality

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