MATH 3395 Lecture Notes - Lecture 4: Parallelogram, Isosceles Trapezoid, Adbc
25 Sep 2017
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#1: the opposite sides of a parallelogram are congruent. Since bc ad (cid:883) (cid:884) (because parallel lines imply alternate interior angles). Cd, (cid:885) (cid:886)(because parallel lines imply alternate interior angles). Hence, ab cd and bc ad since corresponding parts of congruent triangles are congruent (cpctc). #2 the diagonals of a parallelogram bisect each other. Bm md and am mc are congruent because (cid:886) (cid:885) are alternate interior angles and. Because the angles are alternate interior angles it means the diagonals are congruent and bisect each other. M is also the midpoint of the two lines. Since the side lengths are equal they bisect each other. #3: the diagonals of a rhombus are perpendicular. Each angle is 90 degrees because 360/4 is 90. All sides are based on definition of a rhombs. Dma dmc bma bmc are congruent based on cpctc. Since the angles are 90 degrees it proves that bd ac.
