Chapter 2 Reasoning and Proof

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

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.

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.

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.

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

Example Complete each proof.

Example Complete each proof.

Example

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.

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.

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

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