Identifying a Parallelogram: Using the theorem: If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is considered a parallelogram

Examples with solutions for Identifying a Parallelogram: Using the theorem: If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is considered a parallelogram

Exercise #1

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

AAABBBDDDCCC134615

Is it possible to conclude that this quadrilateral is a parallelogram?

Video Solution

Step-by-Step Solution

According to the properties of a parallelogram, each pair of opposite sides are parallel and equal to each other.

Since the data shows that each pair of sides are not equal to each other, the quadrilateral is not a parallelogram.

1513 15\ne13

46 4\ne6

Answer

No.

Exercise #2

Look at the quadrilateral ABCD.

AB = 6

CD = 6

BD = 4

AC = 4

AAABBBDDDCCC6446

Is this quadrilateral a parallelogram?

Video Solution

Answer

Yes

Exercise #3

Shown below is the quadrilateral ABCD.

AB = 7 and CD = 6.

BD = 3 and AC = 4.

AAABBBDDDCCC6437

Is the quadrilateral a parallelogram?

Video Solution

Answer

No.

Exercise #4

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 15.

BD = 10 and AC = 10.

AAABBBDDDCCC15101015

Is the quadrilateral a parallelogram?

Video Solution

Answer

Yes.

Exercise #5

Look at the quadrilateral ABCD shown below.

AB = 10 and CD = 8.

BD = 7 and AC = 6.

AAABBBDDDCCC86710

Is the quadrilateral a parallelogram?

Video Solution

Answer

No.

Exercise #6

Shown below is the quadrilateral ABCD.

AB = 20 and CD = 20.

BD = 8 and AC = 8.

AAABBBDDDCCC208820

Is the quadrilateral a parallelogram?

Video Solution

Answer

Yes

Exercise #7

ABCD is a quadrilateral.

AB = 11 and CD = 11.

BD = 4 and AC = 4.

AAABBBDDDCCC114411

Is the quadrilateral a parallelogram?

Video Solution

Answer

Yes.

Exercise #8

Shown below is the quadrilateral ABCD.

AB = 7 and CD = 6.

BD = 2 and AC = 3.

AAABBBDDDCCC6327

Is the quadrilateral a parallelogram?

Video Solution

Answer

No.

Exercise #9

Look at the quadrilateral ABCD.

AB = 15

CD = 12

BD = 7

AC = 8

AAABBBDDDCCC128715

Is this quadrilateral a parallelogram?

Video Solution

Answer

No

Exercise #10

Shown below is the quadrilateral ABCD.

AB = 12 and CD = 12.

BD = 6

AC = 6

AAABBBDDDCCC126612

Is the quadrilateral a parallelogram?

Video Solution

Answer

Yes.

Exercise #11

Below is the quadrilateral ABCD.

AB = 10 and CD = 8.

BD = 2 and AC = 4.

AAABBBDDDCCC84210

Is the quadrilateral a parallelogram?

Video Solution

Answer

No