How to Prove That a Quadrilateral is a Parallelogram

With Everyone’s favorite

parallelogram, Spongebob!

Panos TsaklasPaul ChengSection 5.6Mod. 7

Proving a quadrilateral to be a paralellogram is so easy, a caveman could

do it!

• All you have to do, is remember 5 easy methods.

Method # 1

• If both pairs of opposites sides are parallel, then the quadrilateral is a parallelogram.

Method # 2

• If both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram.

Method # 3

• If one pair of opposite sides are parallel AND congruent, then the quadrilateral is a parallelogram.

Method # 4

• If the diagonals in a quadrilateral bisect each other, then it is a parallelogram.

Method # 5

• If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

• The following diagram is an example of the fifth method, if both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

• This diagram is a parallelogram because of both methods 1 and 4. Since both pairs of opposite sides are parallel, method 1 works, and since the diagonals bisect each other, method 4 works.

Given: Triangle CAR is isosceles, with base CR AC is congruent to BK <C is congruent to <KProve: BARK is a parallelogram

Example ProofCAR Is isos. w/ base CR1. 1. Given

2. AC AR 2. Legs of an isos. are 3. AC BK 3. given

4. ARBK4. Transitive Property

5. <C <ARC5. Base <‘s of an isos. Triangle are congruent

6. <C <K6. Given

7. <ARC <K7. Transitive Property

8.AR Is parallel toBK8. Corr. <‘s congruent implies parallel lines

9. BARK is a parallelogram9. If one pair of opposite sides of a quadrilateral are both parallel and congruent, it is a parallelogram

• What method(s) would be used to prove that this quadrilateral is a parallelogram?

• If you guessed methods 2 and 5, you’re correct! Since both pairs of opposite sides are congruent, method 2 works, and since both pairs of opposite angles are congruent, method 5 works!

• What method(s) would be used to prove that this quadrilateral is a parallelogram?

• If you guessed method 3, you’re correct! Method 3 works because at least one pair of opposite sides are both parallel and congruent.

• Still confused on how to prove that a quadrilateral is a parallelogram? If so, check out this video:

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