6.3 Proving Quadrilaterals are Parallelograms

Theorem If both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram.

Theorem If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.

Theorem If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.

Theorem If consecutive angles in a quadrilateral are supplementary, then it is a parallelogram.

Theorem If the diagonals of a quadrilateral bisect each other, then it is a parallelogram

Theorem If one pair of opposite sides in a quadrilateral are parallel and congruent, then it is a parallelogram.

Given

Given: Prove: #1. #1. Given

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of #3.

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of #3.#3. //, Alt. Int. angles

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of #3.#3. //, Alt. Int. angles #4.HL = IK

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of #3.#3. //, Alt. Int. angles #4.HL = IK#4.C.P. C. T.

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of #3.#3. //, Alt. Int. angles #4.HL = IK#4.C.P. C. T. #5.

Given: Prove: #1. #1. Given #2. HJ//MK #2. Def of #3.#3. //, Alt. Int. angles #4.HL = IK#4.C.P. C. T. #5. #5.one side // and

Show points A:(- 1,2), B:(3,2), C:(1,-2), D:( -3,-2) Makes a Parallelogram.

Homework Page #10 – 26 even 32,

Homework Page 342 – 346 #9 – 27 odd, 40, 42 – 47, 42 – 47, Quiz #1 problems, #1 - 4