1 / 10

Given: AB = CD 1/5 AD = CB

C. B. Given: AB = CD 1/5 AD = CB Prove: ABCD is a parallelogram hint: congruent triangles, alt interior angles conv. <1. <3. <4. <2. D. A. statement reason AB = CD given AD = CB given

donnarsmith
Download Presentation

Given: AB = CD 1/5 AD = CB

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. C B Given: AB = CD 1/5 AD = CB Prove: ABCD is a parallelogram hint: congruent triangles, alt interior angles conv <1 <3 <4 <2 D A statement reason AB = CD given AD = CB given Draw AC through any two points there exists exactly one line

  2. C B Given: AB = CD AD = CB Prove: ABCD is a parallelogram <1 <3 <4 <2 D A statement reason AB = CD given AD = CB given Draw AC through any two points there exists exactly one line AC = AC reflexive property ∆ABC = ∆CDA SSS <1 = <2 CPCTC BC // DA alternate interior angles converse <3 = <4 CPCTC AB // CD alternate interior angles converse ABCD is a parallelogram definition of a parallelogram

  3. C B Given: <B = <D 2/5 <A = <C Prove: ABCD is a parallelogram hint: quad sum thm, consec angle conv D A statement reason <B = <D given <A = <C given

  4. C B Given: <B = <D <A = <C Prove: ABCD is a parallelogram D A statement reason <B = <D given <A = <C given <A +<B +<C + <D = 360 quadrilateral sum theorem <A + <B + <A + <B = 360 substitution 2<A + 2<B = 360 combine like terms 2(<A + <B) = 360 distributive property <A + <B = 180 division property BC // DA consecutive interior angles converse <A + <D + <A + <D = 360 substitution 2<A + 2<D = 360 combine like terms 2(<A + <D) = 360 distributive property <A + <D = 180 division property AB // CD consecutive interior angles converse ABCD is a parallelogram definition of a parallelogram

  5. C B Given: <A + <B = 180 3/5 <A + <D = 180 Prove: ABCD is a parallelogram D A statement reason <A + <B = 180 given <A + <D = 180 given

  6. C B Given: <A + <B = 180 <A + <D = 180 Prove: ABCD is a parallelogram D A statement reason <A + <B = 180 given <A + <D = 180 given BC // DA consecutive interior angles converse AB // CD consecutive interior angles converse ABCD is a parallelogram definition of a parallelogram

  7. C B Given: AE = CE 4/5 BE = DE Prove: BC // DA hint: congruent triangles, alt interior angles conv E D A statement reason AE = CE given BE = DE given

  8. C B Given: AE = CE BE = DE Prove: BC // DA E D A statement reason AE = CE given BE = DE given <BEC = <DEA vertical angle theorem ∆AED = ∆CEB SAS <ADE = <CBE CPCTC BC // DA alternate interior angles converse

  9. C B Given: AE = CE 5/5 BE = DE Prove: ABCD is a parallelogram hint: 2 pairs of congruent triangles, alt interior angles conv E D A statement reason AE = CE given BE = DE given

  10. C B Given: AE = CE BE = DE Prove: ABCD is a parallelogram E D A statement reason AE = CE given BE = DE given <BEC = <DEA vertical angle theorem ∆AED = ∆CEB SAS <ADE = <CBE CPCTC BC // DA alternate interior angles converse <BEA = <DEC vertical angle theorem ∆AEB = ∆CED SAS <ABE = <CDE CPCTC AB // CD alternate interior angles converse ABCD is a parallelogram definition of a parallelogram

More Related