Section 6 2 Properties of Parallelograms OBJECTIVES To

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 C 8 B 8 A in the figure? D E 12 F

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

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