Introduction to Proof: Informal and Two Column Proofs

Two Column Proofs in Geometry

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Example:

Remember the trick you learned about identifying supplementary angles in section 1?  We're going to prove it now.

In the figure below, line AB is parallel to line CD.  Prove that the sum of angle ADF and angle CGE is 180 degrees.

= line A B parallel to line C D, cut by transversal F E at point D on line A B and point G on line C D

Statement Reason
line A B parallel line C D Given
angle A D F and angle C G F are corresponding anglesDefinition of corresponding angles
angle A D F is congruent to angle C G FCorresponding angles are congruent
angle C G E and angle C G F are supplementary anglesDefinition of supplementary angles
measure of angle C G E plus measure of angle C G F equals 180Supplementary angles add to 180 degrees
measure of angle C G E plus measure of angle A D F equals 180Using (3), Substitution property
measure of angle A D F plus measure of angle C G F equals 180Commutative property