6.2: Properties of Parallelograms Objectives: To use relationships among sides and among angles of parallelograms To use relationships involving diagonals of parallelograms or transversals
Please note… • Every property that you learn in this section also applies to rectangles, rhombuses and squares!!!!! They are part of the Parallelogram Family! • The converse of every theorem in this section is also true.
THEOREM: Opposite sides of a parallelogram ( ) are congruent.
Example: Given EFGH Find GH and EG 7 E F 6 G H
Theorem: Opposite angles of a are congruent. W V T U
EXAMPLE C J 115 65 G H FIND measure of angle J and angle H.
Consecutive Angles • Angles that share a side D C A B
In a parallelogram, consecutive angles are supplementary (Because they are same-side interior angles!!) D C A B
Find the values of the variables. b+7 c+4 2c 60° (3a)° 18
Theorem: The diagonals of a bisect each other. E F K H G Example: If EK = 4 and HK = 7, find KG and KF
The figure below is a parallelogram. Find the value of x. A 2x-1 AD=26 D
The figure below is a parallelogram. Find the values of x and y. 2x+3 6y-16 4y 4x-9
Theorem If one pair of opposite sides of a quadrilateral is BOTH congruent and parallel, then the quadrilateral is a parallelogram. EXAMPLES: Is there enough information to determine that the quadrilateral is a parallelogram? Explain. a.) b.) x x
Graph the parallelogram. Reflect it over the x –axis. A(1,4), B(3,5) , C(6,1), D(4,0)
Theorem: If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on EVERY transversal.