Properties of Parallelograms
Warm Up 3/17 Find the perimeter of triangle ABC: B 4 cm 3 cm 6 cm 2x cm x + 4 cm 4 cm A C
Definition Parallelogram – a quadrilateral with both pairs of opposite sides parallel.
Theorem: Opposite Sides If a quadrilateral is a parallelogram, then its opposite sides are congruent. and
Theorem: Opposite Angles If a quadrilateral is a parallelogram, then its opposite angles are congruent. P R and Q S
Theorem: Consecutive Angles If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. m P + m Q = 180 , m Q + m R = 180 , m R + m S = 180 , m S + m P = 180
Theorem: Bisecting Diagonals If a quadrilateral is a parallelogram, then its diagonals bisect each other. and
Example 1 FHGJ is a parallelogram. Find the unknown length. JG= JK=
Example 2 PQRS is a parallelogram. Find the angle measure. m R = m Q =
Example 3 ABCD is a parallelogram. Find x.
Example 4 Given the figure is a parallelogram find the value of x and y 84 o (3x+3) o 2y o
Example 5 ABCD is a parallelogram. The diagonals intersect at point E. Use the given information to solve for the variables m, n and x. CE = 3m AE = 15 A D C B E
Summarizer Name 5 properties of parallelograms 1. opposite sides parallel 2. opposite sides congruent 3. opposite angles congruent 4. consecutive angles supplementary 5. diagonals bisect each other