Can a quadrilateral ABCD be a parallelogram if (i) ∠D + ∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) ∠A = 70° and ∠C = 65°? (2024)

FAQs

Can a quadrilateral ABCD be a parallelogram if anglea angleb 180? ›

The sum of the measures of the adjacent angles should be 180° and opposite angles should also be of the same measure. Hence, using the given condition ∠D + ∠B = 180° we can say that yes, it may or may not be a parallelogram. (ii) Property of parallelogram: The opposite sides of a parallelogram are of equal length.

Hint: As we know that the opposite sides of parallelogram is equal so we apply and check this condition on this given parallelogram, as AB=DC=8cm, these 2 sides are same but we have to check for other two sides AD=4cm and BC=4.4cm are not equal so it will not be a parallelogram.

Since opposite angles are equal in parallelogram and here opposite angles are not equal in quadrilateral ABCD. Therefore it is not a parallelogram.

Given a Quadrilateral ABCD with ∠ A = 70° and ∠C = 65° We know, Opposite angles of a Parallelogram are equal. ∠C = ∠A But ∠A ≠ ∠ C So, ABCD is not a parallelogram.

The angles in a parallelogram add to 360 degrees. This stems from the fact that opposite sides are parallel creating 2 pairs of consecutive interior angles. Each pair of consecutive interior angles have a sum of 180 degrees on their own. When added together the total is 360 degrees.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If — BD and — AC bisect each other, then ABCD is a parallelogram.

It has four sides, in which two pairs of sides are parallel. Also, the parallel sides are equal in length. If the length of the parallel sides is not equal in measurement, then the shape is not a parallelogram. Similarly, the opposite interior angles of a parallelogram should always be equal.

Answer: Yes, it can parallelogram. As we know that opposite sides of parallelogram is equal and sum of its adjacent angles be 180 degrees.

We can say that a quadrilateral is a closed figure with four sides : e.g. ABCD is a quadrilateral which has four sides AB, BC, CD and DA, four angles ∠A,∠B,∠C and ∠D and four vertices A, B, C and D and also has two diagonals AC and BD. i.e. A quadrilateral has four sides, four angles, four vertices and two diagonals.

Review Definition of a parallelogram - A quadrilateral with 2 pair of parallel sides is called a parallelogram. ABCD is a p-gram. Theorem 5-4 If both pair of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Is a quadrilateral a parallelogram yes or no? ›

No. Every parallelogram is a quadrilateral, but a quadrilateral is only a parallelogram if it has specific characteristics, such as opposite sides are parallel and congruent, opposite angles are congruent, adjacent angles are supplementary, and the diagonals bisecting each other.

In a parallelogram if two diagonals are equal, then the parallelogram is a rectangle.So, ABCD is a rectangle.It is known that each interior angle of a rectangle is 90 degree. Since ABC is an interior angle of rectangle ABCD, so measure of angle ABC is 90 degree.

Solution: i) Yes, for ∠D+∠B=180° ABCD can be a parallelogram if ∠D+∠A=180°or∠B+∠A=180°.

Explanation: In Mathematics, specifically in geometry, a quadrilateral ABCD is a parallelogram if opposite sides are equal in length (i.e., AB = DC and BC = AD), or if opposite angles are equal (i.e., ∠A = ∠C and ∠B = ∠D), or if one pair of opposite sides are both parallel and equal (i.e., AB || DC and AB = DC).

By the property of a triangle, it has three sides and three angles also known as trigon, the root word “tri” means “three”. Quadrilaterals have four sides and four angles, the root word “quad” means “four”. Hence, a triangle will never be a quadrilateral, because they do not share traits and the properties.

One pair of opposite sides is parallel and congruent. Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. The diagonals bisect each other.

However, even though parallelograms do not have line symmetry, they do have rotational symmetry since any parallelogram, after a rotation of 180 degrees, will result in the exact same image as you started with.