- 1). Sketch the geometric figure that is being described within the geometry proof. In order to do a two-column geometry proof, you have to see a depiction of the geometric figure in order to apply the axioms and theorems, as well as observe relationships about the next steps you need to take in order to finish the proof. If the geometric figure is already provided, then analyze it. If the figure is not provided, draw it according to the description of the proof and then examine it. You can examine the figure by marking the congruent sides, congruent angles or right angles.
- 2). Write down the information that is given. Before making the proof table, you need to become familiar with the information about the geometric figure that has already been provided. For example, you may be presented with a triangle with a line at the center that bisects the base of the triangle. The overall triangle is labeled QRX, and the line is line QB. Q is at the point of the triangle, R is the right corner and X is the left corner. Your given information may be that line segment QB is perpendicular to line segment RX, and that line segment QB bisects line segment RX. Write this down.
- 3). Write down the objective you are attempting to prove. In order to do a two-column geometry proof, you need to know what you are trying to prove. For example, you may be asked to prove that triangle QRB is congruent to triangle QXB. Write this down.
- 4). Make your proof table. In order to do a two-column geometry proof, you need to make a table that has two separate columns. Label one column "Statements" and the other column "Reasons." This will help you to organize your information.
- 5). Determine the steps you need to take in order to solve the two-column geometry proof. In order to do a two-column geometry proof, use the information that you are provided with and try to find ways to incorporate facts into your thought process. For example, in the "Statement" column, write that line segment QB bisects line segment RX. In the "Reason" column, write "Given." This will enable you to see that B is the midpoint of line segment RX. Therefore, in the "Statement" column, write this. In the "Reason" column, write "Definition of a segment bisector."
- 6). Continue to observe relationships among the components of the geometric figure. For example, a midpoint divides a line segment into two congruent segments. Therefore, line segment BX is congruent to line segment BR. Write this in the "Statement" column. In the "Reason" column, write "Definition of a midpoint." Mark a single line on segments BX and BR to show that they are congruent. Also, triangles QBX and QBR share line segment QB. In the "Statement" column, write that line segment QB is congruent to itself. In the "Reason" column, write "Reflective Axiom." Put two small lines on line segment QB in order to show that the triangles share this line segment.
- 7). Use the remainder of your given information to arrive at a resolution. For example, in the "Statement" column, write that line segment QB is perpendicular to line segment RX. In the "Reason" column, write "Given." Then, in the "Reason" column, write that angles QBX and QBR are right angles. In the "Reason" column, write "Definition of perpendicular lines." Then, in the "Statement" column, write that angle QBX is congruent to angle QBR. In the "Reason" column, write "Right angles are congruent." Mark angles QBX and QBR in order to show that they are congruent.
- 8). Examine your picture in order to arrive at your concluding statement of the proof. Your objective was to prove that triangle QBX is congruent to triangle QBR. You have proven that two sides and the included angle of triangle QBX are congruent to the corresponding parts of triangle QBR. This is the Side Angle Side (SAS) axiom. Therefore, in the "Statement" column, write that triangle QBR is congruent to triangle QBX. In the "Reason" column, write "Side Angle Side (SAS) axiom."
Source...