Theorems/postulates
By: dhruv Sethi
Corresponding angles theorem
Definition: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Understanding: Since lines R and S are parallel and cut by a transversal, angles 1 and 2 are congruent because they are corresponding angles.
*I chose this theorem because it really applies to geometric proofs.
Understanding: Since lines R and S are parallel and cut by a transversal, angles 1 and 2 are congruent because they are corresponding angles.
*I chose this theorem because it really applies to geometric proofs.
Alternate interior angles theorem
Definition: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Understanding: Since lines R and S are parallel and are cut by a transversal, angles 1 and 2 are congruent because they are alternate interior angles.
*I chose this theorem because it is a very logical and interesting one.
Understanding: Since lines R and S are parallel and are cut by a transversal, angles 1 and 2 are congruent because they are alternate interior angles.
*I chose this theorem because it is a very logical and interesting one.
Alternate exterior angles theorem
Definition: If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent.
Understanding: Since lines R and S are parallel and cut by a transversal, angles 1 and 2 are congruent because they are alternate interior angles.
*i chose this theorem because it is an effective theorem in proofs.
Understanding: Since lines R and S are parallel and cut by a transversal, angles 1 and 2 are congruent because they are alternate interior angles.
*i chose this theorem because it is an effective theorem in proofs.
Same-side interior angles theorem
Definition: If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary.
Understanding: Since lines R and S are parallel and cut by a transversal, angles 1 and 2 are supplementary because the are same-side interior angles.
*I chose this theorem because it applies supplementary angles and can be linked and used with algebra.
Understanding: Since lines R and S are parallel and cut by a transversal, angles 1 and 2 are supplementary because the are same-side interior angles.
*I chose this theorem because it applies supplementary angles and can be linked and used with algebra.
Linear pair theorem
Definition: If two angles form a linear pair, then they are supplementary.
Understanding: Since <ABC and <CBD are a linear pair, they equal 180 degrees and are thus supplementary.
*I chose this theorem because it lays the foundation for supplementary angles yet it is quite basic.
Understanding: Since <ABC and <CBD are a linear pair, they equal 180 degrees and are thus supplementary.
*I chose this theorem because it lays the foundation for supplementary angles yet it is quite basic.
Parallel postulate
Definition: Through a point C not on line L, there is exactly one line parallel to L.
Understanding: Since point C is not on line L, there is 1 and only 1 line that can be drawn that is parallel to L.
*I chose this postulate because it is different in Euclidean geometry than it is in Spherical geometry.
Understanding: Since point C is not on line L, there is 1 and only 1 line that can be drawn that is parallel to L.
*I chose this postulate because it is different in Euclidean geometry than it is in Spherical geometry.