definition of a parallelogram opposite sides of parallelogram are congruent opposite angles of a parallelogram are congruent diagonals of a parallelogram bisect each other alternate interior angles theorem consecutive interior angles theorem alternate interior angles theorem converse consecutive interior angles theorem converse definition of a rhombus

C B Given: ABCD is a parallelogram 1/7 Prove: AB = CD AD = CB <1 <3 <4 <2 D A statement reason ABCD is a parallelogram given Draw AC through any two points there exists exactly one line

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

C B Given: ABCD is a parallelogram 2/7 Prove: <B = <D hint: opp sides of parallelogram are cong <1 <3 <4 <2 D A statement reason ABCD is a parallelogram given Draw AC through any two points there exists exactly one line

C B Given: ABCD is a parallelogram 2/5 Prove: <B = <D hint: opp sides of parallel are cong <1 <3 <4 <2 D A statement reason ABCD is a parallelogram given Draw AC through any two points there exists exactly one line AB = CD opposite sides of parallelogram are congruent BC = DA opposite sides of parallelogram are congruent AC = AC reflexive property ∆ABC = ∆CDA SSS <B = <D CPCTC

C B Given: ABCD is a parallelogram 3/7 Prove: AE = CE BE = DE <1 <3 E <4 <2 D A statement reason ABCD is a parallelogram given

C B Given: ABCD is a parallelogram 5/5 Prove: AE = CE BE = DE <1 <3 E <4 <2 D A statement reason ABCD is a parallelogram given <1 = <2 alternate interior angles theorem <3 = <4 alternate interior angles theorem BC = DA opposite sides of parallelogram are congruent ∆BCE = ∆DAE ASA AE = CE CPCTC BE = DE CPCTC

C B Given: BC // DA BC = DA Prove: ABCD is a parallelogram <3 4/7 <4 <2 <1 D A statement reason BC // DA given BC = DA given

C B Given: BC // DA BC = DA Prove: ABCD is a parallelogram <3 <4 <2 <1 D A statement reason BC // DA given BC = DA given <1 = <3 alternate interior angles theorem AC = AC reflexive property ∆ABC = ∆CDA SAS <2 = <4 CPCTC AB // CD alternate interior angles converse ABCD is a parallelogram definition of a parallelogram

C B Given: ABCD is a parallelogram AC BD Prove: AB = AD 5/7 E D A Note: figure not drawn to scale statement reason ABCD is a parallelogram given AC BD given

C B Given: ABCD is a parallelogram AC BD Prove: AB = AD E D A Note: figure not drawn to scale statement reason ABCD is a parallelogram given AC BD given BE = DE diagonals of a parallelogram bisect <AEB = 90 definition of lines <AED = 90 definition of lines <AEB = <AED substitution AE = AE reflexive property ∆AEB = ∆AED SAS AB = AD CPCTC

C B Given: ABCD is a rhombus Prove: <AEB = 90 6/7 E D A Note: figure not drawn to scale statement reason ABCD is a rhombus given

C B Given: ABCD is a rhombus Prove: <AEB = 90 E D A Note: figure not drawn to scale statement reason ABCD is a rhombus given AB = BC definition of a rhombus AE = CE diagonals of a rhombus bisect each other BE = BE reflexive property ∆ABE = ∆CBE SSS <AEB = <CEB CPCTC <AEB + <CEB = 180 linear pair postulate <AEB + <AEB = 180 substitution 2(<AEB) = 180 combine like terms <AEB = 90 division property

B C Given: ABCD is a parallelogram AC = BD Prove: <A = 90 7/7 A D statement reason ABCD is a parallelogram given AC = BD given

B C Given: ABCD is a parallelogram AC = BD Prove: <A = 90 A D statement reason ABCD is a parallelogram given AC = BD given AD = BC opposite sides of a parallelogram are equal AB = AB reflexive property ∆ABD = ∆BAC SSS <A = <B CPCTC BC // DA definition of a parallelogram <A + <B = 180 same side interior angles theorem <A + <A = 180 substitution 2(<A) = 180 combine like terms <A = 90 division property