Chapter 5: Quadrilaterals Chapter 5: Quadrilaterals 5-1: Parallelograms Day 2 Proving the Parallelogram Theorems

Prove: Opposite sides of a parallelogram are congruent A B Steps: Draw a picture State the given Finish proof 3 4 1 2 C D Statements Reasons ABCD is a Draw Given Between 2 pts there’s 1 line Reflexive Property Definition of a || lines imply that alt int ASA CPCTC

Prove: Opposite angles of a parallelogram are congruent A B D C Statements Reasons ABCD is a Draw Given Between 2 pts there’s 1 line Reflexive Property Opposites sides of a are SSS CPCTC

Prove: Diagonals of a parallelogram bisect each other 3 4 E 2 D 1 Statements C Reasons ABCD is a Draw E is a midpoint bisect each other Given Between 2 pts there’s 1 line Definition of || lines imply that alt int Opposites sides of a are ASA CPCTC Definition of midpoint Definition segment bisector

2 1 A B C D X Y Given: Prove: Statements Reasons ABCD is a ;

W X 1 Given: P 3 4 Prove: Q 2 Z Y Statements Reasons

Homework Page 169 & 170: 16, 29-34 Note: for 33 - Prove for 34 - Prove