1. Math 3 Unit 3 Lesson: Proofs: Flow, Paragraph and Two Column
Know:
Methods of proving triangles are congruent.
Proofs are a way to demonstrate meathematical reasoning.
Be able to:
Write a flow proof and/or paragraph proving a quadrilateral is a parallelgram.

2. Learning Resources
RegentsPrep.org
Holt McDougal Geometry

3. Two Column Proofs Flow Proofs Paragraph proofs
Proofs are developed such that each step in the argument is in proper chronological order in relation to earlier steps. 
When building a proof, be sure that your argument is clearly developed and that each step is supported by a property, theorem, postulate or definition. 
Remember to write a proof as if the reader knows nothing about geometry. 
Two Column Proofs
Flow Proofs
Paragraph proofs

4. Step-by-Step Instructions for Writing Two-Column Proofs
1) Read the problem and note the givens and the question.
2) Draw a picture with the correct markings.
2) List your detailed statements and their reasons.
3) Ensure you are answering the right question.
4) Go back and proofread your proof..

5. Prove Δ𝐴𝐶𝐸≅Δ𝐴𝐷𝐵 given that ∠𝐷≅∠𝐶
and 𝐵𝐷 ≅ 𝐶𝐸
Statement
Justification

6. Given that NRSM is a parallelogram and ∠4 ≅∠5, prove ERAM is also a parallelogram.

8. Flow Chart Proof
Uses boxes and connecting arrows to display the information and show the order

9. Flow Chart Proof
Prove Δ𝐴𝐶𝐸≅Δ𝐴𝐷𝐵 given that ∠𝐷≅∠𝐶
and 𝐵𝐷 ≅ 𝐶𝐸

10. Given that NRSM is a parallelogram and ∠4 ≅∠6, prove ERAM is also a parallelogram.
Flow Chart Proof

11. The Paragraph Proof

12. Caution: Easy to make mistakes and difficult to check your work for errors.
The Paragraph Proof
Given: E is the midpoint of 𝑩𝑫 and 𝑨𝑬 ≅ 𝑬𝑪
Prove: 𝚫𝑨𝑬𝑩≅𝚫𝑫𝑬𝑪
We are given the figure above and the facts that E is the midpoint of 𝑩𝑫 and that 𝑨𝑬 ≅ 𝑬𝑪 . Since E is the midpoint of 𝐵𝐷 , we know that 𝑩𝑬 ≅ 𝑬𝑫 because the midpoint of a segment divides the segment into two congruent segments. Since vertical angles are congruent, ∠𝑩𝑬𝑨≅∠𝑪𝑬𝑫. We now have sufficient information to satisfy the SAS method of proving triangles congruent. 𝜟𝑩𝑬𝑨≅𝜟𝑪𝑬𝑫 because if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

13. More examples of two column proofs
More examples of flow chart Proofs
More examples of paragraph proofs

14. Homework More Practice: Aleks M3U3L03 HW 1 Proofs And
Write the same proof using Two Column, Flow, and paragraph style proofs.