1. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Today you will need:
Your notes
Your textbook

2. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Quadrilateral – A 4-sided polygon
Parallelogram – A quadrilateral where each pair of opposite sides are parallel

3. Module 9, Lessons 9.1 and 9.2 - Parallelograms
-In order to prove facts about parallelograms (or most other shapes), we must apply what we know about triangles.
-We can do this by creating diagonals (lines that connect the opposite vertices of the figure)
What do we know about the two triangles created?
They are congruent by…
ASA!

4. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Page 421
Given
Definition of a Parallelogram
Alternate Interior Angle Theorem
Reflexive Property of Congruence
∆𝐴𝐷𝐵≅∆𝐶𝐵𝐷
CPCTC

5. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Page 422
Given
Through any two points, there is exactly one line.
Definition of a parallelogram
∠𝐴𝐷𝐵≅∠𝐶𝐵𝐷, ∠𝐴𝐵𝐷≅∠𝐶𝐷𝐵
𝐷𝐵≅𝐷𝐵
∆𝐴𝐷𝐵≅∆𝐶𝐵𝐷
∠𝐴≅∠𝐶
CPCTC

6. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Think about what we already know is congruent in a parallelogram. Can we prove the diagonals bisect each other?

7. Module 9, Lessons 9.1 and 9.2 – Parallelograms (pg. 427)
AC bisects DB and DB bisects AC
Given
𝐴𝐵≅𝐷𝐶 and 𝐴𝐷≅𝐵𝐶
Opposite sides of a parallelogram are congruent
∠𝐴𝐷𝐵≅∠𝐶𝐵𝐷, ∠𝐴𝐵𝐷≅∠𝐶𝐷𝐵
∠𝐷𝐴𝐶≅∠𝐵𝐶𝐴, ∠𝐷𝐶𝐴≅∠𝐵𝐴𝐶
Alternate Interior Angle Theorem
∆𝐴𝐸𝐵≅∆𝐶𝐸𝐷, ∆𝐴𝐸𝐷≅∆𝐶𝐸𝐵
ASA Triangle Congruence
CPCTC
AC bisects DB and DB bisects AC
Definition of a bisector

8. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Consecutive angles of a parallelogram are SUPPLEMENTARY
X + X + Y + Y = 360° X° Y°
2X + 2Y = 360° 2
X + Y = 180° Y° X°

9. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Facts about Parallelograms – Summary
Module 9, Lessons 9.1 and Parallelograms
CONGRUENT
Opposite sides of a parallelogram are both parallel and _________________
CONGRUENT
Opposite angles of a parallelogram are _________________
SUPPLEMENTARY
Consecutive angles of a parallelogram are _________________
BISECT EACH OTHER
The diagonals of a parallelogram ____________________________
CONGRUENT
The diagonals of a parallelogram are not necessarily _________________

10. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Facts about Parallelograms – Converses
Module 9, Lessons 9.1 and Parallelograms

11. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Page 425
Module 9, Lessons 9.1 and Parallelograms

12. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Page 427
Module 9, Lessons 9.1 and Parallelograms

13. Module 9, Lessons 9.1 and 9.2 - Parallelograms
Page 427
Module 9, Lessons 9.1 and Parallelograms