Ways to identify the parallelogram - Examples, Exercises and Solutions

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

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

Detailed explanation

Practice Ways to identify the parallelogram

Question 1

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

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

Question 2

Given the quadrilateral ABCD that:

$$ ∢A=100° $$ $$

y $$ ∢C=80° $$

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

Question 3

Given the quadrilateral ABCD that:

$$ ∢D=95° $$ $$

y $$ ∢C=85° $$

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

Question 4

Given the quadrilateral ABCD that:

$$ ∢A=115° $$ $$

y $$ ∢D=115° $$

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

Question 5

Given the quadrilateral ABCD that:

$$ ∢A=110° $$ $$

y $$ ∢D=110° $$

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

examples with solutions for ways to identify the parallelogram

Exercise #1

Shown below is the quadrilateral ABCD.

AB = 15 and CD = 13.

BD = 6 and AC = 4

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.

$15\ne13$

$4\ne6$

Answer

No.

Exercise #2

Given the quadrilateral ABCD that:

$∢A=100°$

y $∢C=80°$

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 on angle B or angle D.

Therefore, the quadrilateral is not a parallelogram.

Answer

Exercise #3

Given the quadrilateral ABCD that:

$∢D=95°$

y $∢C=85°$

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, it is given that angles C and D sum up to 180 degrees but nothing is given about the other angles.

Therefore, we cannot determine if the sides are parallel to each other.

As a result, this quadrilateral is not a parallelogram.

Answer

Exercise #4

Given the quadrilateral ABCD that:

$∢A=115°$

y $∢D=115°$

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

Exercise #5

Given the quadrilateral ABCD that:

$∢A=110°$

y $∢D=110°$

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

Video Solution

Step-by-Step Solution

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

As a result, the quadrilateral is not a parallelogram.

Answer

Question 1

Given the quadrilateral ABCD that:

$$ ∢D=120° $$ $$

y $$ ∢B=70° $$

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

Question 2

Given the quadrilateral ABCD that:

$$ ∢A=100° $$ $$

y $$ ∢C=70° $$

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

Question 3

Given the quadrilateral ABCD that:

$$ ∢B=45° $$ $$

y $$ ∢D=135° $$

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

Question 4

Given the quadrilateral ABCD that:

$$ ∢D=105° $$ $$

y $$ ∢C=75° $$

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

Question 5

Below is the quadrilateral ABCD:

$$ ∢A=90° $$ $$

$$ ∢C=95° $$

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