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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 <u>addition property</u>
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
∠AGF + ∠AGE = ∠CHE + ∠AGF
Therefore, the measure of ∠AGE is equal to the measure of ∠CHE by <u>addition property of </u><u>equality</u>
- ∠EGB + ∠AGE = ∠AGF + ∠AGE by linear pair angles
Therefore;
∠EGB and ∠AGF are congruent by the<u> addition property</u> of equality
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