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

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

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!

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

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

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?

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

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°

Module 9, Lessons 9.1 and 9.2 - Parallelograms Facts about Parallelograms – Summary Module 9, Lessons 9.1 and 9.2 - 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 _________________

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

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

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

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