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Geometry Section 6-2A Proofs with Parallelograms

Geometry Section 6-2A Proofs with Parallelograms. Proofs with Parallelograms:.

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Geometry Section 6-2A Proofs with Parallelograms

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  1. Geometry Section 6-2A Proofs with Parallelograms

  2. Proofs with Parallelograms: We have been working on developing skills in writing proofs. Each proof has become increasingly difficult and you have been asked to fill in more and more as time has gone by. You must continue to build this skill so that you can write a proof from scratch all by yourself.

  3. Proofs: 5 steps to writing a proof. 1. Rewrite 2. Draw 3. State (“Given” and “Prove”) 4. Plan a. Think backwards. b. Do you need to prove things about congruent angles, parallel lines, triangles, etc? 5. Demonstrate (Write the proof)

  4. We have not spent as much time on the planning steps as we have on the other steps. Today we will focus on that as well as writing a proof from scratch. We will be focusing on parallelograms because they have many properties that you know well. a. mÐPMN 135o b. mÐMNO 45o c. mÐOPM 45o d. MP e. OP f. MQ g. NQ 7 15 5.5 10.5

  5. Writing a Proof Prove: The opposite angles of a parallelogram are congruent. Rewrite: If then a quadrilateral is a parallelogram, its opposite angles are congruent. Draw: A B D C State: Given:Prove: ABCD is a parallelogram ÐABC @ÐCDA, ÐDAB @ÐBCD Plan: If we can divide this into 2 triangles and prove that they are congruent, then we can use CPCTC to match up congruent angles. How do we divide this into 2 triangles? Draw an auxiliary line.

  6. B A Given:Prove: ABCD is a parallelogram ÐABC @ÐCDA, ÐBAD @ÐBCD D C ABCD is a parallelogram Given Draw AC Two pts. determine a line ABDC Def. of parallelogram ADBC Def. of parallelogram ÐACD @ÐCAB Alt. Int. Бs are @. ÐDAC @ÐBCA Alt. Int. Бs are @. AC@AC Reflexive Property DABC @DCDA ASA ÐABC @ÐCDA CPCTC Two pts. determine a line Draw BD ÐABD @ÐBDC Alt. Int. Бs are @. ÐADB @ÐDBC Alt. Int. Бs are @. BD@BD Reflexive Property DBAD @DBCD ASA ÐBAD @ÐBCD CPCTC

  7. Properties of Parallelograms: 1. Opposite sides of a parallelogram are parallel. 2. Opposite angles of a parallelogram are congruent. 3. Opposite sides of a parallelogram are congruent. 4. Consecutive angles of a parallelogram are supplementary. 5. Diagonals of a parallelogram bisect each other.

  8. If I give you 3 dots on a coordinate grid, how many different parallelograms could we make?

  9. Homework: Practice 6-2AChange #12 to Prove: AB @ CD and BC @ AD

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