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Section 6.4

Section 6.4. Proving Quadrilaterals are Parallel. Theorems. Thm 6.7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

zachery-dejesus
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Section 6.4

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  1. Section 6.4 Proving Quadrilaterals are Parallel

  2. Theorems Thm 6.7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram Thm6.8: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram Thm6.9: If an angle of a quadrilateral is supplementary to both consecutive angles, then the quadrilateral is a parallelogram Thm6.10: If the diagonal of a quadrilateral bisects each other, then the quadrilateral is a parallelogram

  3. Ex: prove Thm 6.7 1. Given: AB ≌CD, AD≌ BC Prove: ABCD is a 1. AB ≌CD, AD ≌ BC 1.given 2. AC≌ AC 2. reflexive 3. <1 ≌ <2 3. par lines. Alt int <‘s ≌ 4. ∆ABC≌∆CDA 4. SAS 5. AD≌ CB 5. CPCTC 6. ABCD is a 6. quad w/ both pairs opp sides ≌ is a

  4. Ex Prove Thm 6.10 2. Given: AC & BD bisect each other Prove: ABCD is a 1. AC & BD bisect each other 1. given 2. AE≌ CE, BE≌DE 2. def of seg bisector 3. <1 ≌ <2, <3≌ <4 3. vert <‘s are ≌ 4. ∆ADE ≌ ∆CBE,∆DEC ≌∆BEA 4. SAS 5. AD≌ CB, DC ≌BA 5. CPCTC 6. ABCD is a par 6. quad w/ both pairs of opp sides ≌ is a par

  5. Thm 6.11 If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.

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