Section 6.2 Properties of Parallelograms OBJECTIVES: To use relationships among sides and angles of parallelograms. To use relationships among diagonals of parallelograms. BIG IDEA: Reasoning and Proof ESSENTIAL UNDERSTANDINGS: Parallelograms have special properties regarding their sides, angles, and diagonals. Parallelograms can be used to prove theorems about parallel lines and their transversals. MATHEMATICAL PRACTICE: Construct viable arguments and critique the reasoning of others

Math Background The study of polygons is a study of hierarchy. Quadrilaterals are a subset of polygons and parallelograms are a subset of quadrilaterals. Thus parallelograms have all properties of polygons and quadrilaterals as well as special properties of their own. Parallelogram: a _________________________ with both pairs of ____________________ sides ____________________ Opposite sides do not share a vertex Opposite angles do not share a side Consecutive angles share a side

Theorems about Parallelograms THM 6.3: If a quadrilateral is a parallelogram, then its ____________________ sides are ____________________ THM 6.4: If a quadrilateral is a parallelogram, then its ____________________ angles are ____________________ THM 6.5: If a quadrilateral is a parallelogram, then its ____________________ angles are ____________________ THM 6.6: If a quadrilateral is a parallelogram, then its ____________________ bisect each other

Theorem THM 6.7: If three (or more) ____________________ lines cut off ____________________ segments on one _____________________, then they cut off ____________________ segments on every transversal EX: What are in the figure? C D 8 B E 8 12 A F

EX: Find the measure in the parallelogram HIJK. Explain your reasoning. 1. HI 7. KH H K 2. GH 8. HJ 3. 16 G 7 4. 8 I J 10 5. 6.

EX: Find the value of each variable in the parallelogram 9. 10.

EX: Find the value of each variable in the parallelogram 11. 12.

EX: Given: Prove: Statements Reasons