1. Chapter 2
Reasoning and Proof

2. 2.5/2.6 Algebraic Proof
Postulate – a statement that is accepted as true
Through any 2 points there is exactly 1 line
A line contains at least two points
Through any 3 non-collinear points there is exactly one plane
A plane contains at least 3 non-collinear points

3. 2.5/2.6 Algebraic Proof
If 2 points lie in a plane, the entire line containing those points must lie in the plane.
If 2 lines intersect, their intersection is a point.
If 2 planes intersect, their intersection is a line.

4. Example
Determine whether each statement is always, sometimes, or never true. Explain.
1. If points A, B, and C lie in plane M, then they are collinear.
2. There is exactly one plane that contains non-collinear points P, Q, and R.

5. Example
Determine whether each statement is always, sometimes, or never true. Explain.
3. There are at least two lines through points M and N.
4. If two coplanar lines intersect, then the point of intersection lies in the same plane as the two lines.

6. Example
Determine whether each statement is always, sometimes, or never true. Explain.
5. 𝑮𝑯 contains three non-collinear points.

8. Example
Complete each proof.

9. Example
Complete each proof.

10. Example

11. Example State the property that justifies each statement.
1. If 𝑚∠𝐴=𝑚∠𝐵 and 𝑚∠𝐵=𝑚∠𝐶, 𝑚∠𝐴=𝑚∠𝐶.
2. If 𝐻𝐽+5=20, then 𝐻𝐽=15.
3. If 𝑋𝑌+20=𝑌𝑊 and 𝑋𝑌+20=𝐷𝑇, then 𝑌𝑊=𝐷𝑇.

12. Example State the property that justifies each statement.
4. If 2 𝑥− 3 2 =5, then 2𝑥−3=5.
5. If 𝑚∠1+𝑚∠2=90 and 𝑚∠2=𝑚∠3, then 𝑚∠1+𝑚∠3=90.

13. Example Write a two column proof.
6. If 𝐴𝐶=𝐴𝐵, 𝐴𝐶=4𝑥+1, and 𝐴𝐵=6𝑥−13, then 𝑥=7.

14. Example Write a two column proof. 7. Given: ∠𝐴≅∠𝐵, 𝑚∠𝐴=110
Prove: ∠𝐵=110