1 / 5

Proving Quadrilaterals are Parallelograms: Key Theorems and Proof Strategies

This resource explores essential theorems for proving quadrilaterals are parallelograms. Thm. 6.7 states that if both pairs of opposite sides are congruent, the quadrilateral is a parallelogram. Thm. 6.8 asserts that congruent opposite angles imply the same. Thm. 6.9 indicates if one angle is supplementary to its consecutive angles, the quadrilateral is a parallelogram. Lastly, Thm. 6.10 explains that if the diagonals bisect each other, the quadrilateral is also a parallelogram. Detailed proofs for these theorems are included.

zachery-dejesus
Télécharger la présentation

Proving Quadrilaterals are Parallelograms: Key Theorems and Proof Strategies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related