Identifying a Parallelogram - Examples, Exercises and Solutions

Question Types:
Identifying a Parallelogram: Using the properties of the perimeter of the parallelogramIdentifying a Parallelogram: Using angle propertiesIdentifying a Parallelogram: Using the theorem: If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is considered a parallelogramIdentifying a Parallelogram: Identification by diagonalsIdentifying a Parallelogram: Identification by one pair of sides

We can identify that the square in front of us is a parallelogram if at least one of the following conditions is met:

  1. If in a square each pair of opposite sides are parallel to each other, the square is a parallelogram.
  2. If in a square each pair of opposite sides are equal to each other, the square is a parallelogram.
  3. If a square has a pair of opposite sides that are equal and parallel, the square is a parallelogram.
  4. If in the square the diagonals intersect, the square is a parallelogram.
  5. If in a square there are two pairs of equal opposite angles, the square is a parallelogram.

Diagram illustrating the properties of a parallelogram: opposite sides are parallel and equal, opposite angles are equal, and diagonals bisect each other. Visual aid for understanding ways to identify a parallelogram, featured in a geometry guide.

Detailed explanation

Suggested Topics to Practice in Advance

  1. Parallelogram

Practice Identifying a Parallelogram

Question 1

Given the quadrilateral ABCD where:

\( ∢A=100° \)\( \)

y \( ∢C=80° \)

AAABBBDDDCCC100°80°

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

Question 2

Given the quadrilateral ABCD where:

\( ∢A=110° \)\( \)

y \( ∢D=110° \)

AAABBBDDDCCC110°110°

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

Question 3

Given the quadrilateral ABCD where:

\( ∢A=115° \)\( \)

y \( ∢D=115° \)

AAABBBDDDCCC115°115°

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

Question 4

Given the quadrilateral ABCD where:

\( ∢D=95° \)\( \)

y \( ∢C=85° \)

AAABBBDDDCCC95°85°

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

Question 5

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?

Examples with solutions for Identifying a Parallelogram

Exercise #1

Given the quadrilateral ABCD where:

∢A=100° ∢A=100°

y ∢C=80° ∢C=80°

AAABBBDDDCCC100°80°

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

Video Solution

Step-by-Step Solution

A parallelogram is a quadrilateral whose two pairs of sides are parallel.

Since we know that angles A and C add up to 180 degrees, we know that AB is parallel to CD.

We have no way to prove if AC is parallel to BD since we have no data regarding angle B or angle D.

Therefore, the quadrilateral is not a parallelogram.

Answer

No

Exercise #2

Given the quadrilateral ABCD where:

∢A=110° ∢A=110°

y ∢D=110° ∢D=110°

AAABBBDDDCCC110°110°

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

Video Solution

Step-by-Step Solution

Since we do not have data regarding the other angles, we cannot prove whether the square has opposite sides equal to one other.

As a result, the quadrilateral is not a parallelogram.

Answer

No

Exercise #3

Given the quadrilateral ABCD where:

∢A=115° ∢A=115°

y ∢D=115° ∢D=115°

AAABBBDDDCCC115°115°

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

Video Solution

Step-by-Step Solution

Given that a parallelogram is a quadrilateral whose two pairs of sides are parallel, and in the figure only two angles are given to us.

We do not have enough data to determine and prove whether angles C and B are equal to each other.

Therefore, the quadrilateral is not a parallelogram.

Answer

No

Exercise #4

Given the quadrilateral ABCD where:

∢D=95° ∢D=95°

y ∢C=85° ∢C=85°

AAABBBDDDCCC95°85°

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

Video Solution

Step-by-Step Solution

A parallelogram is a quadrilateral whose two pairs of sides are parallel.

In the figure, we are shown that the sum of angles C and D is 180 degrees but nothing is shared about the other angles.

Therefore, we cannot determine whether or not the sides are parallel to one other.

As a result, this quadrilateral is not a parallelogram.

Answer

No

Exercise #5

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.

15≠13 15\ne13

4≠6 4\ne6

Answer

No.

Question 1

Below is the quadrilateral ABCD:

\( ∢A=90° \)\( \)

\( ∢C=95° \)

AAABBBDDDCCC90°95°

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

Question 2

Given the quadrilateral ABCD that:

\( ∢A=100° \)\( \)

y \( ∢C=70° \)

AAABBBDDDCCC100°70°

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

Question 3

Given the quadrilateral ABCD that:

\( ∢A=100° \)\( \)

y \( ∢D=100° \)

AAABBBDDDCCC100°100°

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

Question 4

Given the quadrilateral ABCD that:

\( ∢A=80° \)\( \)

y \( ∢C=80° \)

AAABBBDDDCCC80°80°

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

Question 5

Given the quadrilateral ABCD that:

\( ∢B=100° \)\( \)

y \( ∢C=80° \)

AAABBBDDDCCC100°80°

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

Exercise #6

Below is the quadrilateral ABCD:

∢A=90° ∢A=90°

∢C=95° ∢C=95°

AAABBBDDDCCC90°95°

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

Video Solution

Answer

No

Exercise #7

Given the quadrilateral ABCD that:

∢A=100° ∢A=100°

y ∢C=70° ∢C=70°

AAABBBDDDCCC100°70°

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

Video Solution

Answer

No

Exercise #8

Given the quadrilateral ABCD that:

∢A=100° ∢A=100°

y ∢D=100° ∢D=100°

AAABBBDDDCCC100°100°

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

Video Solution

Answer

No

Exercise #9

Given the quadrilateral ABCD that:

∢A=80° ∢A=80°

y ∢C=80° ∢C=80°

AAABBBDDDCCC80°80°

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

Video Solution

Answer

No

Exercise #10

Given the quadrilateral ABCD that:

∢B=100° ∢B=100°

y ∢C=80° ∢C=80°

AAABBBDDDCCC100°80°

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

Video Solution

Answer

No

Question 1

Given the quadrilateral ABCD that:

\( ∢B=45° \)\( \)

y \( ∢D=135° \)

AAABBBDDDCCC135°45°

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

Question 2

Given the quadrilateral ABCD that:

\( ∢D=105° \)\( \)

y \( ∢C=75° \)

AAABBBDDDCCC105°75°

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

Question 3

Given the quadrilateral ABCD that:

\( ∢D=120° \)\( \)

y \( ∢B=70° \)

AAABBBDDDCCC120°70°

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

Question 4

ABCD is a quadrilateral.

AB = 11 and CD = 11.

BD = 4 and AC = 4.

AAABBBDDDCCC114411

Is the quadrilateral a parallelogram?

Question 5

Below is the quadrilateral ABCD.

AB = 10 and CD = 8.

BD = 2 and AC = 4.

AAABBBDDDCCC84210

Is the quadrilateral a parallelogram?

Exercise #11

Given the quadrilateral ABCD that:

∢B=45° ∢B=45°

y ∢D=135° ∢D=135°

AAABBBDDDCCC135°45°

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

Video Solution

Answer

No

Exercise #12

Given the quadrilateral ABCD that:

∢D=105° ∢D=105°

y ∢C=75° ∢C=75°

AAABBBDDDCCC105°75°

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

Video Solution

Answer

No

Exercise #13

Given the quadrilateral ABCD that:

∢D=120° ∢D=120°

y ∢B=70° ∢B=70°

AAABBBDDDCCC120°70°

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

Video Solution

Answer

No

Exercise #14

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 #15

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