# L2.12 - Proofs about Quadrilaterals

## Learning Intentions and Success Criteria

We are learning to:

- Comprehend a conjecture and express it (in writing) as a specific statement to prove.
- Critique others' reasoning (in spoken and written language) about quadrilaterals.
- Prove (in writing) theorems about quadrilaterals.

- Critique a proof about quadrilaterals.
- Prove theorems about quadrilaterals.
- Rewrite a conjecture so it is specific enough to prove.

## 12.1: Play with Parallelograms

Open BOOK - Geo.2.12 Proofs about Quadrilaterals. Use the applet to explore the 4 quadrilaterals.

1. Which figures (if any) are always rectangles? Which figures can be dragged to make a rectangle?

2. Which figures (if any) are always parallelograms? Which figures can be dragged to make a parallelogram?

## Six Properties of Parallelograms

- Opposite sides are congruent (AB DC).
- Opposite angles are congruent (D B).
- Consecutive angles are supplementary (mA + mD = 180°).
- If one angle is right, then all angles are right.
- The diagonals of a parallelogram bisect each other.
- Each diagonal of a parallelogram separates it into two congruent triangles.

## Show the Properties of Parallelograms 1, 2, 3, & 4 in this applet.

Write an explanation in detail for properties of parallelograms 1, 2, 3, & 4.

## Show Property 5 of Parallelograms (The diagonals of a parallelogram bisect each other.)

## Write an explanation in detail for property 5 of parallelograms.

5. The diagonals of a parallelogram bisect each other.

## Show Property of Parallelograms 6 (Each diagonal of a parallelogram separates it into two congruent triangles.)

## Write an explanation in detail for property 6 of parallelograms.

6. Each diagonal of a parallelogram separates it into two congruent triangles.

## Learning Intentions and Success Criteria

We are learning to:

- Comprehend a conjecture and express it (in writing) as a specific statement to prove.
- Critique others' reasoning (in spoken and written language) about quadrilaterals.
- Prove (in writing) theorems about quadrilaterals.

- Critique a proof about quadrilaterals.
- Prove theorems about quadrilaterals.
- Rewrite a conjecture so it is specific enough to prove.

## Cool-Down: A Proof In Time Saves Nine

Elena wants to prove that a quadrilateral with 4 right angles must have congruent opposite sides. Explain to Elena how she can use the fact that all rectangles are parallelograms in her proof.