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How to Teach Deductive Geometry

Deductive proofs in geometry help students to learn critical thinking skills. You teach them beginning with introducing the concept of if-then statements where the students are given a set of conditions from which they can find new information. For example, if all professional baseball players wear a uniform during all games and Carlos Beltran is a professional baseball player, then he wears a uniform during all games. In geometry, you can teach students deductive proofs by giving them a set of conditions related to points, lines and shapes, joined together at different angles. After you teach the if-then concept, you move on to introduce and explain a set of theorems and postulates using illustrations that assist in creating new information about a given geometrical object. When you model, you write out statements and reasons, step by step, until what you are given and what you want to find out are proved. Finally, you have students solve similar geometry proofs based on the set of theorems and postulates you have covered. Once they become proficient at solving one set of problems (such as those dealing with lines), you move on to more difficult sets.

Things You'll Need

  • Smartboard
  • Whiteboard
  • Textbooks
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Instructions

    • 1

      Draw out the geometrical figure given in a textbook or worksheet. For example, if you find a problem where C is given as midpoint of line AB, you can draw any size "line AB" with a ruler.

    • 2

      Write what you want to prove. For example, you can demonstrate that you want to prove is that line AC is what fraction of AB and line CB is what fraction of line AB.

    • 3

      Teach students how you make all the assumptions that you think you know about the figure. Introduce term "deducing." Illustrate with a drawing that C is in the middle and your total line AB is 6 inches, then you can teach that you can deduct C as being 3 inches long. You can then mark point C 3 inches from point A.

    • 4

      Draw two columns on the whiteboard. Above one column, write "Statements" and above the other, write "Reasons".

    • 5

      Write each step to solve the proof in the appropriate columns. For example, the first statement is the given, "C is the midpoint of line AB." The first reason is "given." The second statement is AC = CB. The second reason is that the statement is the definition of a midpoint. The third statement is AC + CB = AB. The third reason is that this is a postulate known as the "segment addition." The third statement is AC + AC = 2AC, which is the same as saying 2AC = AB. The reason is known as the "substitution property." The fourth statement is that AC = 1/2 AB. The reason is the "division property." Finally, CB = 1/2 AB, with the reason again being the "division property."

    • 6

      Repeat the process for another problem related to the theorems and postulates you've covered in the past. For example, you can model proving that the opposite angles of two intersecting lines are equal.

    • 7

      Give students similar proofs to solve related to the theorems and postulates in you've modeled. After you've given proofs to solve, show students the correct way to solve the proof.

K-12 Basics
K-12 Basics
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