Bellwork The given figure is a parallelogram Solve

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

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 A D STATEMENTS 1. Quadrilateral ABCD, AB ≅ CD, AB ІІ CD B C REASONS 2. BAC ≅ DCA 1. Given 2. Parallel lines form alternate interior angles 3. AC≅CA 3. Reflexive Property 4. ∆ABC≅∆CDA 4. SAS 5. DAC ≅ BCA 6. AD ІІ CB 7. ABCD is a parallelogram 5. CPCTC 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 X W STATEMENTS Y Z REASONS 1. WX ≅ ZY and XY ≅ WZ 1. Given 2. ∆WXZ≅∆YZX 2. SSS 3. WXZ ≅ YZX 3. CPCTC 4. WX ІІ ZY 4. If alternate interior angles are congruent then lines are parallel. 5. WX ІІ ZY, WX ≅ ZY 6. WXYZ is a parallelogram 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