Is a quadrilateral with equal sides a parallelogram?

The square is a special parallelogram, the quadrilateral with equal sides is not necessarily a parallelogram, the condition is that the two opposite sides are equal is the parallelogram, if it is not equal to the opposite sides, it may not be a parallelogram, if it is a diamond, the special condition that the four sides are equal is a special parallelogram, look at the theorem more, these things are different and related.

A parallelogram contains a rectangle, which in turn contains a square.

The 4 sides of the square are equal and the 4 corners are all right angles.

The opposite sides of the rectangle are equal to each other, and the 4 corners are all right angles.

A parallelogram is equal on opposite sides.

The definition of a parallelogram is: a parallelogram in the same plane with two sets of opposing sides parallel to each other is called a parallelogram.

Premise of judgment: within the same plane.

Judgment content: 1) Two sets of quadrilaterals with equal opposite sides are parallelograms;

2) a set of quadrilaterals with opposite sides parallel and equal is a parallelogram;

3) Two sets of quadrilaterals with opposite sides parallel to each other are parallelograms;

4) A quadrilateral with two diagonals bisecting each other is a parallelogram.

In the same plane, these conditions are mutually restrictive, e.g., two sets of opposing edges are equal, and two sets of opposing edges must be parallel; One set of opposing edges is parallel and equal, and the other set of opposing edges is also parallel and equal.

Differences: Rectangles, squares, and diamonds are all special parallelograms, and squares are special rectangles.

The rectangle is a parallelogram with equal sides and all four corners at right angles. A square is a parallelogram with all four sides equal and all four corners at right angles.

A rhombus is a parallelogram with all four sides equal.

A quadrilateral with equal opposite sides is not necessarily a parallelogram.

Definition of parallelogram: A parallelogram is a closed graph composed of two sets of parallel lines on the same two-dimensional plane, usually named by the name of the figure plus four vertices in turn. The opposite side or opposite side of a parallelogram is equal in length, and they are equal in diagonal.

Only a quadrilateral with a pair of parallel sides is trapezoidal, and its three-dimensional counterpart is a parallelepiped. This type of figure is characterized by being parallel to the opposite sides and equal, and it is easy to deform.

The Parallelogram Rule: The way to judge a parallelogram is to prove that two pairs of sides are parallel, the two pairs of sides are equal, the two pairs of sides are parallel and equal, and the diagonals are equal. In general, a parallelogram is named by its dispatch shape name plus four vertices.

When two vectors are combined, a parallelogram is made with the line segments representing the two vectors as adjacent edges, and the diagonal of this parallelogram represents the magnitude and direction of the stupid vector before synthesis, which is called the parallelogram rule.

Determine if the parallelogram is axisymmetric: The parallelogram is not axisymmetric, but it is a center-symmetrical figure. The center of symmetry is the intersection of two diagonals.

An axisymmetric figure is defined as a figure that is folded along a straight line in a plane, and the parts on both sides of the line can coincide exactly. A straight line is called the axis of symmetry, and the axis of symmetry is represented by a dashed line; At this time, we also say that the figure is about the symmetry of this straight line. Such as circles, squares, isosceles triangles, equilateral triangles, isosceles trapezoids, etc.

In quadrilaterals, rectangles, squares, and parallelograms are all quadrilaterals with equal opposite sides.

Quadrilaterals with equal sides areParallel quadruple trigramsTarget. Two sets of quadrilaterals that are parallel and equal to each other are called parallelograms. Two sets of quadrilaterals with opposite sides parallel to each other are parallelograms.

According to the nature of the parallelogram, the two groups of opposite sides of the parallelogram are parallel, and the two groups of opposite sides are equal; It can be concluded that two sets of quadrilaterals with equal opposite sides are parallelograms.

Introduction to parallelograms

The opposite sides of the parallelogram are parallel and therefore never intersect. The area of a parallelogram is determined by its diagonal.

One creates twice the area of the triangle.

The area of the parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides. Any line that touches the midpoint through the parallelogram family bisects the region. Any non-degenerate affine transformation.

All use parallelograms of parallelograms.

The parallelogram has rotational symmetry of order 2. If it also has two-row reflective symmetry, then it must be diamond-shaped or rectangular. If it has four lines of reflective symmetry, it is a square.

The circumference of the parallelogram is 2(a + b), where a and b are the lengths of the adjacent sides.

There are several ways to determine a parallelogram:

1. The two groups of opposite sides are equal;

2. A set of opposite sides is parallel and equal;

3. The diagonals are bisected with each other;

4. The diagonal of the two groups of skin type is equal.

If only the two sides of the slag grip are equal, this condition is not enough.

Yes. The method of determining the parallelogram is as follows:

1. Two groups of quadrilaterals with opposite sides parallel to each other are parallelograms (definition and judgment method);

2) a set of quadrilaterals with opposite sides parallel and equal is a parallelogram;

3. Two sets of quadrilaterals with equal opposite sides are parallelograms (this is true only when the plane quadrilaterals are true, if it is not a plane quadrilateral, even if it is two groups of quadrilaterals with equal opposite sides, it is not a parallelogram. ）

4. Two groups of quadrilaterals with equal diagonal angles are parallelograms (two groups of opposite sides are judged to be parallel);

5. A quadrilateral with diagonals bisecting each other is a parallelogram.

Features of the parallelogram:

1. Parallelograms belong to plane figures.

2. Parallelograms belong to quadrilaterals.

3. The parallelogram belongs to the center symmetry figure.

Extended Materials. Properties of parallelograms:

1. If a quadrilateral is a parallelogram, then the two groups of opposite sides of the quadrilateral are equal to each other. (Simply described as "two sets of opposite sides of a parallelogram are equal.")

2. If a quadrilateral is a parallelogram, then the two sets of diagonal diagonals of this quadrilateral are equal. (Shortly described as "two groups of diagonal opposites of a parallelogram that accompany each other and sing each other, etc.").

3. If a quadrilateral is a parallelogram, then the adjacent angles of this quadrilateral complement each other. (Briefly described as "Adjacent Angles of Parallelograms Complementary").

4. The parallel height sandwiched between two parallel lines is equal. (Simply described as "the high distances between parallel lines are equal everywhere").

5. If a quadrilateral is a parallelogram, then the two diagonals of this quadrilateral are bisected from each other.

A quadrilateral with two opposing sides equal is a parallelogram, because if the two opposing sides are equal, then the two opposing sides must be parallel.

According to the judgment of the parallelogram in the book, two sets of quadrilaterals with equal sides are parallelograms

By the way, the judgment of the parallelogram is completely scraped:

Two sets of quadrilaterals with opposite sides parallel to each other are parallelograms.

A set of quadrilaterals that are parallel and equal to the opposite sides is a parallelogram.

Two groups of quadrilaterals with opposite sides closing and losing equal amounts are parallelograms.

A quadrilateral with two diagonals bisecting each other is a parallelogram.

Two sets of quadrilaterals with equal diagonal angles are parallelograms.

The quadrilateral that the center pair Qingming calls is a parallelogram.