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Introduction to Geometry Proofs

Introduction to Geometry Proofs. Proof Vocabulary. Axiom Postulate Theorem Click here to look up these words on Merriam Webster’s website. Write them in your Geometry notebook in your own words. Look in the appendices in your textbook and find an example of each.

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Introduction to Geometry Proofs

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  1. Introduction to Geometry Proofs

  2. Proof Vocabulary • Axiom • Postulate • Theorem • Click here to look up these words on Merriam Webster’s website. Write them in your Geometry notebook in your own words. • Look in the appendices in your textbook and find an example of each.

  3. Logical Argument in AlgebraClick here to watch an example. • Given x + y = 60 • Given x = 5 • Prove y = 55 • Use your algebra knowledge to write a proof. Justify each step you write.

  4. Follow the steps. x + y = 60 x = 5 5 + y = 60 y = 55 Justify the steps. Given Given Substitution Property of Equality Subtraction Property of Equality Algebra Proof Solution

  5. Types of Geometry ProofVocabulary cards are at Classzone.com • Paragraph Proofs • Find an example in your textbook and read it to your table partner. • Flow Chart Proofs • Find an example in your textbook and copy the steps into your Geometry notebook. • Two Column Proofs • This third example is the most commonly used type of proof. We will focus on this type of proof in class.

  6. Paragraph Proof • Given BA ┴ BC • Prove angle 3 and 4 are complementary A D 3 4 B C Because BA ┴ BC, angle ABC is a ________ and the measure = _______. According to the ________ Postulate, the measure of angle 3 + the measure of angle 4 = the measure of angle ABC. So, by the substitution property of equality, ________ + ________ = ________. By definition, angle 3 and angle 4 are complementary.

  7. Flow Chart Proofs j 5 6 k Given: angle 5 is congruent to angle 6, angle 5 and 6 are a linear pair. Prove: j is perpendicular to k. Put the following statements in the proper order to complete the proof. When you have finished, compare your solution to your partners. j is perpendicular to k 2(measure of 5) = 180° measure of 5 = 90° angle 5 is congruent to angle 6 measure of 5 + measure of 6 = 180° measure of 5 + measure of 5 = 180° angle 5 and angle 6 are supplementary measure of 5 = measure of 6 angles 5 and 6 are a linear pair. angle 5 is a right angle

  8. Flow Chart Proofs j 5 6 k Given: angle 5 is congruent to angle 6, angle 5 and 6 are a linear pair. Prove: j is perpendicular to k. • Now that you have the statements in a logical order, add a reason to each statement. Reasons are based on properties, postulates and theorems. • When you have finished, bring your paper to the teacher. You will be asked to explain your reasoning.

  9. Statements In this column we write the logical steps that lead us to the end result. Reasons For each statement, we must use a postulate or theorem that supports the statement. Two Column ProofsAsk Dr. Math is a great place to start.

  10. Statements A is an angle. Measure of A = Measure of A Angle A is congruent to Angle A Reasons ______________________ ______________________ ______________________ Two Column ProofFill in the blanks to complete the proof of the Reflexive Property of the Congruence of Angles.

  11. Statements A is an angle. Measure of A = Measure of A Angle A is congruent to Angle A Reasons Given Reflexive Property of Equality Definition of Congruent Angles Two Column Proof Check your solution for the proof of the Reflexive Property of the Congruence of Angles.

  12. One last 2 Column Proof n m 2 3 1 Complete the following proof by filling in the blanks. Given: Angle 1 and Angle 2 are supplementaryProve: n is parallel to m Statements Reasons 1) Angle 1 and Angle 2 are supplementary. 1)______________________ 2) Angle 1 and Angle 3 are a linear pair. 2)______________________ 3)_____________________________ 3) Linear Pair Postulate 4)_____________________________ 4) Congruent Supplements Theorem 5) n is parallel to m. 5) ______________________

  13. One last 2 Column Proof n m 2 3 1 Check your work to see how well you are doing. Given: Angle 1 and Angle 2 are supplementaryProve: n is parallel to m Statements Reasons 1) Angle 1 and Angle 2 are supplementary. 1) Given 2) Angle 1 and Angle 3 are a linear pair. 2) Definition of Linear Pair 3) Angle 1 and Angle 3 are supplementary. 3) Linear Pair Postulate 4) Angle 2 is congruent to Angle 3 4) Congruent Supplements Theorem 5) n is parallel to m. 5) Corresponding Angles Converse

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