What are the sufficient conditions for a quadrilateral to be a parallelogram?
If both pairs of opposite sides of a quadrilateral are parallel, then it’s a parallelogram (reverse of the definition). If both pairs of opposite sides of a quadrilateral are congruent, then it’s a parallelogram (converse of a property).
How do you prove that 4 coordinates are a parallelogram?
Let the points (4, 5) (7, 6) (4, 3) (1, 2) represent the points A, B, C and D. Opposite sides of the quadrilateral formed by the given four points are equal. Also the diagonals are unequal. Therefore, the given points form a parallelogram.
Do all parallelograms have 4 yes or no sides?
A Parallelogram can be defined as a quadrilateral whose two s sides are parallel to each other and all the four angles at the vertices are not 90 degrees or right angles, then the quadrilateral is called a parallelogram. The opposite sides of parallelogram are also equal in length.
How do you know if 4 points form a quadrilateral?
Number of quadrilaterals possible from the given points
- We need to check whether any of the given points are same. If yes, no of quadrilateral = 0.
- Then we need to check whether any of the 3 points of the given 4 points are collinear or not.
- if its a convex quadrilateral then there is only one possible quadrilateral.
What are the 4 properties of a trapezium?
Properties of Trapezium
- It is a 2D shape.
- The bases of a trapezium are parallel to each other.
- The length of both the diagonals is equal.
- The diagonals of a trapezium always intersect each other.
- The adjacent interior angles sum up to 180°.
- The sum of all the interior angles in a trapezium is always 360°.
What are the basic properties of a parallelogram?
The parallelogram has the following properties: Opposite sides are parallel by definition. Opposite sides are congruent. Opposite angles are congruent.
Do parallelograms have 4 right angles?
A parallelogram has two parallel pairs of opposite sides. A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A rhombus is defined as a parallelogram with four equal sides.
What are the conditions for a quadrilateral to be parallelogram?
The document Conditions for a Quadrilateral to be Parallelogram and Mid Point Theorem, Class 9, Mathematics Class 9 Notes | EduRev is a part of Class 9 category. THEOREM-5: If each pair of opposite sides of a quadrilateral is equal, then it is parallelogram.
How to find the properties of a parallelogram?
Theorems on Properties of a Parallelogram. 1 Theorem 1: A diagonal of a parallelogram divides the parallelogram into two congruent triangles. Assume that ABCD is a parallelogram and AC is a 2 Theorem 2: 3 Theorem 3: 4 Theorem 4: 5 Theorem 5:
Which is the converse of Theorem 4 parallelogram?
We can say that Theorem 5 is the converse of Theorem 4. The diagonals of a parallelogram bisect each other. Consider a parallelogram ABCD and draw both the diagonals and it intersects at the point O. Now, measure the lengths, such as OA, OB, OC and OD.
How are the opposite sides of a parallelogram equal?
The opposite sides of a parallelogram are equal in measurement and they are parallel to each other. The opposite angles of a parallelogram are equal. The sum of interior angles of a parallelogram is equal to 360°. The consecutive angles of a parallelogram should be supplementary (180°).