Lesson 6 1 Parallelograms Lesson 6 1 Parallelogram

Lesson 6 -1 Parallelograms Lesson 6 -1: Parallelogram 1

Parallelogram Definition: A quadrilateral whose opposite sides are parallel. B Symbol: a smaller version of a parallelogram C D A Naming: l A parallelogram is named using all four vertices. l You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction. l For example, the figure above can be either ABCD or ADCB. Lesson 6 -1: Parallelogram 2

A Properties of Parallelogram D B P 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other but are not congruent P is the midpoint of C . Lesson 6 -1: Parallelogram 3

H Examples 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. P K M L Draw HKLP. PL and HP = ____ KL HK = _______. P m<K = m<______. P or K = 180. m<L + m<______ 115° 65 and m<L =____. If m<P = 65 , then m<H = 115° ____, m<K = ______ Draw the diagonals with their point of intersection labeled M. 5 units. If HM = 5, then ML = ____ 14 units. If KM = 7, then KP = ____ units. If HL = 15, then ML = 7. 5 ____ If m<HPK = 36 , then m<PKL = _____ 36 ; . (Alternate interior angles are congruent. ) Lesson 6 -1: Parallelogram 4

Sides and Angles Theorem 6. 1: Opposite sides of a parallelogram are congruent. Statements Reasons 1. 2. 3. 4. 5. 6.

Sides and Angles Consecutive angles: angles of a polygon that share a side and are consecutive angles of a parallelogram. They are. Theorem 6. 2: Opposite angles of a parallelogram are congruent.

Diagonals and Transversals Theorem 6. 3: The diagonals of a parallelogram bisect each other. Statements 1. ABCD is a parallelogram 2. 3. Reasons 1. 2. Defn. of a parallelogram 3. 4. 5. 6. 7. 4. 5. ASA Post. 6. 7.

Diagonals and Transversals