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Bellwork ….. The given figure is a parallelogram. Solve for the missing variable

Bellwork ….. The given figure is a parallelogram. Solve for the missing variable. 6). Hint: Alternate interior angles of parallel line cut by a transversal are congruent…. (4c + 5)º. (2c +19)°. 6-3 Proving That a Quadrilateral is a Parallelogram. Theorem 6-5 .

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Bellwork ….. The given figure is a parallelogram. Solve for the missing variable

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  1. Bellwork….. The given figure is a parallelogram. Solve for the missing variable 6) Hint: Alternate interior angles of parallel line cut by a transversal are congruent…. (4c + 5)º (2c +19)°

  2. 6-3 Proving That a Quadrilateral is a Parallelogram

  3. Theorem 6-5 If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram. EX. Is the given figure a parallelogram??

  4. Theorem 6-6 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. EX. Is the given figure a parallelogram??

  5. Theorem 6-7 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. EX. Is the given figure a parallelogram??

  6. Theorem 6-8 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parellelogram. EX. Is the given figure a parallelogram??

  7. Bellwork 7) Determine if the quadrilateral is a parallelogram.

  8. Homework # 11 Determine whether the quadrilateral is a parallelogram. Explain.

  9. Properties that you need to know…… Reflexive Property: AB ≅ AB , A ≅ A Symmetric Property: If AB ≅ CD, then CD≅ AB. If A ≅ B, then B ≅ A. Transitive Property: If AB ≅ CD and CD≅ EF, then AB ≅ EF. If A ≅ B and B ≅ C, then A ≅ C.

  10. Concepts you should know for proofs… -Reflexive property, Symmetric property, Transitive property -SAS,SSS,ASA congruence -CPTPC- Corresponding parts of congruent triangles are congruent

  11. EX. Given: Quadrilateral ABCD AB≅ CD, AB ІІ CD. Prove: ABCD is a parallelogram A B D C 1. Given 2. Parallel lines form alternate interior angles 3. Reflexive Property 4. SAS 5. CPCTC 6. If alternate interior angles are congruent, then lines are parallel 7. Definition of parallelogram

  12. EX. Given: WX ≅ ZY and XY ≅ WZ Prove: WXYZ is a parallelogram X Y W Z WX ≅ ZY and XY ≅ WZ 1. Given ∆WXZ≅∆YZX 2. SSS  WXZ ≅  YZX 3. CPCTC 4. If alternate interior angles are congruent then lines are parallel. WX ІІZY WX ІІ ZY, WX ≅ ZY 5. Reason 4, Given 6. THM 6-6: If one pair of opposite sides are both congruent and parallel, then the quadrilateral is a parallelogram WXYZ is a parallelogram

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