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

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Presentation transcript:

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

6-3 Proving That a Quadrilateral is a Parallelogram

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??

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??

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??

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??

Bellwork 7) Determine if the quadrilateral is a parallelogram.

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

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.

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

EX. Given: Quadrilateral ABCD AB ≅ CD, AB ІІ CD. Prove: ABCD is a parallelogram STATEMENTSREASONS 1. Quadrilateral ABCD, AB ≅ CD, AB ІІ CD 2.  BAC ≅  DCA 3. AC ≅ CA 4. ∆ABC ≅ ∆CDA 5.  DAC ≅  BCA 6. AD ІІ CB 7. ABCD is a parallelogram A CD B 1. Given 2. Parallel lines form alternate interior angles 3. Reflexive Property 5. CPCTC 4. SAS 6. If alternate interior angles are congruent, then lines are parallel 7. Definition of parallelogram

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