Can Adjacent Angles be Congruent

Assumptions in geometry: parallel-ogram constructures

Double sides of a square are divided by a square. When we lengthen the sides of the paralleogram in both direction, we now have two straight line parallels intersected by two straight transverse parallels. Parallelline assumptions will help us to realize that the opposite angles in a paralleogram are equivalent.

Corresponding angles are the same when two straight parallels are intersected around a transverse axis. In addition, the angles are the same. Now, we need to expand our understanding to two straight line parallels intersected by two straight transverse parallels. We' ve got new pairings of corresponding angles. How can we say about the adjacent angles of a paralleogram?

Here, too, the assumptions of the parallel line and the assumptions of straight-line couples can help us. Neighboring angles of a paralleogram together make 180 degree, or they are complementary. Presumption (Parallelogram Presumption I): Opposing angles in a paralleogram are congruent. Assumption (Parallelogram Assumption II): Adjoining angles in a paralleogram are complementary.

Assumption (Parallelogram Assumption III): The opposite sides of a paralleogram have the same length. Assumption (Parallelogram Assumption IV): Diagonal lines of a parallelingogram are halved by the point of cross section. Assumptions in the geometry guess list or for introductory purposes.

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