# How many of the following condition can make a quadrilateral a parallelogram?

If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram. 1. Discussion A quadrilateral has two sides that are 3 cm long and two sides that are 5 cm long. A student states that the quadrilateral must be a parallelogram.

## What are the four conditions for quadrilateral to be a parallelogram?

A quadrilateral is a parallelogram if any one of the following holds. (i) Each pair of opposite sides are parallel. (ii) Each pair of opposite sides are equal. (iii) Each pair of opposite angles are equal.

## Which conditions proves that a quadrilateral is a parallelogram?

Criteria proving a quadrilateral is parallelogram

1) If a quadrilateral has one pair of sides that are both parallel and congruent. 2) If all opposite sides of the quadrilateral are congruent. 3) Both pairs of opposite sides are parallel. 4) Opposite angles are congruent.

## What are the conditions of a parallelogram?

Both pairs of opposite sides are congruent. Both pairs of opposite angles are congruent. The diagonals bisect each other. One angle is supplementary to both its consecutive angles.

## Which of the following quadrilateral can be a parallelogram?

Square, rhombus, and rectangle satisfy all the properties of a parallelogram.

## Is all quadrilaterals are parallelogram?

Incorrect. All parallelograms are quadrilaterals, so if it is a parallelogram, it is also a quadrilateral. The correct answer is that all trapezoids are quadrilaterals.

## How do you prove a quadrilateral is a parallelogram Class 9?

1. The sum of all the four angles of a quadrilateral is 360°.
2. A diagonal of a parallelogram divides it into two congruent triangles.
3. A quadrilateral is a parallelogram if. ...
4. A quadrilateral is a parallelogram if. ...
5. Diagonals of a rectangle bisect each other and they are equal and vice-versa.

## Which one of the following is not a condition of a quadrilateral to be a parallelogram?

Any quadrilateral which does NOT have its opposite sides being parallel is not a parallelogram.

## What are the 7 properties of a parallelogram?

Properties of Parallelograms Explained
• Opposite sides are parallel. ...
• Opposite sides are congruent. ...
• Opposite angles are congruent. ...
• Same-Side interior angles (consecutive angles) are supplementary. ...
• Each diagonal of a parallelogram separates it into two congruent triangles. ...
• The diagonals of a parallelogram bisect each other.

## What is the condition of quadrilateral?

All sides are equal and, opposite sides are parallel to each other. Diagonals bisect each other perpendicularly. Sum of any two adjacent angles is 180°

## What is a quadrilateral Class 8?

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.

## What is a parallelogram Class 9?

A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length.

## Why quadrilateral is a parallelogram?

This is always true. Â Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

## What are the 8 properties of a parallelogram?

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°).

## What are the 6 properties of a parallelogram?

There are six important properties of parallelograms to know:
• Opposite sides are congruent (AB = DC).
• Opposite angels are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.

## How many types of quadrilaterals are there?

There are six basic types of quadrilaterals.
...
• Trapezium.
• Parallelogram.
• Rectangle.
• Rhombus.
• Square.
• Kite.

## What are the 6 types of quadrilaterals?

There are six basic types of quadrilaterals:
• Rectangle.
• Square.
• Parallelogram.
• Rhombus.
• Trapezium.
• Kite.

## How many types of parallelogram are there?

Depending on the properties, there are three special types of parallelogram: Rectangle. Rhombus. Square.

## How many kinds of quadrilaterals are there for Class 8?

Types of Quadrilaterals – Rectangle, Square, Rhombus, Parallelogram | Class 8 Maths.

## Which of the following is true in the condition of a parallelogram?

A simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true: Two pairs of opposite sides are parallel (by definition). Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure.

## How do you prove that ABCD is a parallelogram?

Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D . We know that the sum of the angles of a quadrilateral is 360o. Hence, ABCD is a parallelogram.

## How many types of quadrilaterals are there in class 9?

The seven types of quadrilaterals are parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid.

## What condition makes parallelogram math a rectangle?

A parallelogram with one right angle is a rectangle. A quadrilateral whose diagonals are equal and bisect each other is a rectangle.
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