1. Warm Up A D B C
Grab a packet from the ChromeBook cart, but you’ll need your own paper for the lesson.

2. Parallelograms Def. of a parallelogram:
- A quadrilateral with 2 pairs of parallel sides.
Let’s Conjecture About Parallelograms

3. If a quadrilateral is a parallelogram then. . .
- Opposite sides are congruent
- Opposite angles are congruent
- Diagonals bisect each other
AND- If any of the above is true, then the shape must be a parallelogram! (aka- Converses are true)

4. If one pair of opposite sides are ____________
and ____________, then the quadrilateral is a
parallelogram.
congruent
parallel

5. Use the parallelogram to find the following:
1) If mBCD = 125, find mBAD.
2) If mABC = 50, find mBCD.
3) If AB = 5x – 3 and CD = 2x + 9, find AB.
4) If mBCD = x + 40 and mBAD = 3x – 12, find mBAD.
5) Find x and y.
125
130 17 66
x = 20, y = 12

6. Proof of Theorems: “Opposite Sides in a Parallelogram are Congruent”
Given: Parallelogram MAUI
Prove: 𝐴𝑈 ≅ 𝐼𝑀 , ∠𝐴≅∠𝐼, M I

7. E L Y P A Proof of Theorem:
“Diagonals in a parallelogram bisect each other” E L
Given: Parallelogram YELP
Prove: A Y P

8. Proof of Converses of Theorem: “If the opposite sides in a quadrilateral are congruent, then it is a parallelogram” A U
Given: 𝐴𝑈 ≅ 𝐼𝑀 , 𝐴𝑀 ≅ 𝑈𝐼
Prove: MAUI is a parallelogram M I

9. Proof of Converses of Theorem: “If the opposite angles in a quadrilateral are congruent, then it is a parallelogram” A U
Given: ∠𝐴≅∠𝐼,
∠𝑀≅∠𝑈
Prove: MAUI is a parallelogram M I
Let’s just talk it through, rather than writing a formal proof.