Examples with solutions for Identifying a Parallelogram: Using angle properties

Exercise #1

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 #2

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 #3

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 #4

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 #5

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 #6

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 #7

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 #8

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 #9

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 #10

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 #11

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