Ex 3.3, 3 - Can ABCD be a parallelogram if (iii) ∠ A = 70° and ∠C = 65 (2024)

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Ex 3.3, 3 - Can ABCD be a parallelogram if (iii) ∠ A = 70° and ∠C = 65? ›

Ex 3.3, 3 Can a quadrilateral ABCD be a parallelogram if (iii) ∠ A = 70° and ∠C = 65°? 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.

Hence, the condition that opposite angles must be equal is not met. Hence there is a contradiction to our assumption. Hence, quadrilateral ABCD is not a parallelogram.

Step-by-step explanation: opposite angles of a parallelogram are equal, so 1st angle will be 70° . And we know that adjacent angles of a parallelogram are supplementary (lines are parallel): so 2nd angle will be 110°. By this, all angles will be : 70° , 110°, 70° , 110 °. Hope it helps!!

(iii) Property of a parallelogram: In a parallelogram opposite angles are equal. Opposite angles are not equal. So, ABCD is not parallelogram.

Solution. because ∠R and ∠N are opposite angles of a parallelogram. Thus, m∠R = m∠N = 70° and m∠I = m∠G = 110°. Concept: Properties of a Parallelogram - Property: The adjacent angles in a parallelogram are supplementary.

triangles are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Answer: a quadrilateral ABCD is a parallelogram if the opposite sides are equal and parallel to each other.

Opposite angles of rhombus is are equal. Hence, angles of rhombus are 70°, 110°, 70° and 110°.

The remaining angles of the parallelogram are 60∘, 120∘, 120∘.

So, we assume that angle "x" is two-third of angle "y" . We also know that the adjacent sides of a parallelogram are supplementary. It means that the sum of adjacent angles is equal to 180. Hence, the adjacent angles of a parallelogram are 72° and 108° .

Is a parallelogram _ a quadrilateral? ›

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.

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.

In a parallelogram, the adjacent angles are co-interior and the opposite angles are equal. So if one angle is 70°, the angle opposite to this angle is 70°. And the angle adjacent to this angle is supplementary to it. Therefore, the angles of the parallelogram are 70°, 110°, 70° & 110°.

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.

A parallelogram is a quadrilateral whose opposite sides are parallel. The opposite angles of a parallelogram are equal.

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

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).

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.