Presentation on theme: "6-2 Properties of Parallelograms page 294"— Presentation transcript:
16-2 Properties of Parallelograms page 294 Objective: To use relationships among sides, angles, diagonals or transversals of parallelograms.
2Vocabulary Consecutive angles – angles of a polygon that share a side. NOTE: Consecutive angles of a parallelogram are supplementary.ABCD
3You can use what you know about parallel lines & transversals to prove some theorems about parallelogramsTheorem 6.1 p Opposite sides of a parallelogram are congruent
4Theorem 6-1 Opposite sides of a parallelogram are congruent. AB = DC AD = BCABDC
5Properties of Parallelograms Use KMOQ to find m O.Q and O are consecutive angles ofKMOQ, so they are supplementary.Definition of supplementary anglesm O + m Q = 180Substitute 35 for m Q.m O + 35 = 180Subtract 35 from each side.m O = 1456-2
6Theorem 6-2 Opposite angle of a parallelogram are congruent. <A = <C<B = <DABDC
7Find the value of x in ABCD. Then find m A. x + 15 = 135 – xOpposite angles of a are congruent.2x + 15 = 135Add x to each side.2x = 120Subtract 15 from each side.x = 60Divide each side by 2.Substitute 60 for x.m B = = 75Consecutive angles of aparallelogram are supplementary.m A + m B = 180m A + 75 = 180Substitute 75 for m B.Subtract 75 from each side.m A = 1056-2
8Theorem 6-3The diagonals of a parallelogram bisect each other.
9Properties of Parallelograms Find the values of x and y in KLMN.x = 7y – 16The diagonals of a parallelogrambisect each other.2x + 5 = 5y2(7y – 16) + 5 = 5ySubstitute 7y – 16 for x in thesecond equation to solve for y.14y – = 5yDistribute.14y – 27 = 5ySimplify.–27 = –9ySubtract 14y from each side.3 = yDivide each side by –9.x = 7(3) – 16Substitute 3 for y in the firstequation to solve for x.x = 5Simplify.So x = 5 and y = 3.6-2
10Theorem 6-4If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.BD = DFABCDEF
11ClosureLesson 6-1 defined a rectangle as a parallelogram with four right angles. Explain why you can now define a rectangle as a parallelogram with one right angle.
12Summary What is true about the opposite sides of a parallelogram? What is true about the opposite angles of a parallelogram? What about consecutive angles?What about the diagonals of a parallelogram?When 3 or more parallel lines cut of congruent segments on one transversal, what is true about all other transversals?