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

2. Prove: Opposite sides of a parallelogram are congruentA 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

3. Prove: Opposite angles of a parallelogram are congruentA 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

4. Prove: Diagonals of a parallelogram bisect each other3 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

5. 2 1 A B C D X Y
Given:
Prove:
Statements
Reasons
ABCD is a ;

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

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