Create A Rectangle With Unequal Adjacent Sides? Trust The Answer

quadrilateral with two pairs of parallel sides

This article is about the square shape. For the album by Linda Perhacs, see Parallelograms (album)

Parallelogram This parallelogram is a rhomboid because it has no right angles and unequal sides. type quadrilateral, trapezoid edges and corners 4 symmetry group C 2 , [2]+, area b × h (base × height);

ab sin θ (product of neighboring sides and sine of the vertex angle determined by them) properties convex

In Euclidean geometry, a parallelogram is a simple (not self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or opposite sides of a parallelogram are equal in length and the opposite angles of a parallelogram are equal. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate, and no condition can be proved without resorting to the Euclidean parallel postulate or one of its equivalent formulations.

In comparison, a quadrilateral with only one pair of parallel sides is a trapezium in American English or a trapezium in British English.

The three-dimensional counterpart of a parallelogram is a parallelepiped.

The etymology (in Greek παραλληλ-όγραμμον, parallēl-ógrammon, a form “of parallel lines”) reflects the definition.

Special cases[edit]

Rectangle – A parallelogram with four equal angles (right angles).

Rhombus – A parallelogram with four sides of equal length. Any parallelogram that is neither a rectangle nor a rhombus has traditionally been called a rhombus, but this term is not used in modern mathematics. [1]

Square – A parallelogram with four equal sides and equal angles (right angles).

Characterizations[ edit ]

A simple (not self-intersecting) quadrilateral is a parallelogram if and only if one of the following statements is true:[2][3]

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.

The diagonals bisect each other.

A pair of opposite sides are parallel and of equal length.

Adjacent angles are supplementary.

Each diagonal divides the quadrilateral into two congruent triangles.

The sum of the squares of the sides is equal to the sum of the squares of the diagonals. (This is the parallelogram law.)

It has a rotational symmetry of order 2.

The sum of the distances from each interior point to the sides is independent of the location of the point. [4] (This is an extension of Viviani’s theorem.)

(This is an extension of Viviani’s theorem.) There is a point X in the plane of the quadrilateral with the property that any line through X divides the quadrilateral into two regions of equal area.[5]

Thus, all parallelograms have all of the properties listed above, and conversely, if just one of these statements is true in a simple quadrilateral, then it is a parallelogram.

Other properties[ edit ]

Opposite sides of a parallelogram are (by definition) parallel and therefore will never intersect.

The area of ​​a parallelogram is twice the area of ​​a triangle formed from one of its diagonals.

The area of ​​a parallelogram is also equal to the size of the vector cross product of two adjacent sides.

Any line through the center of a parallelogram bisects the area. [6]

Any non-degenerate affine transformation leads one parallelogram to another parallelogram.

A parallelogram has rotational symmetry of order 2 (up to 180°) (or order 4 if it is a square). If it also has exactly two lines of mirror symmetry, it must be a rhombus or a rectangle (a non-square rectangle). If it has four lines of mirror symmetry, it is a square.

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

+ ) where and are the lengths of adjacent sides. Unlike any other convex polygon, a parallelogram cannot be inscribed in any triangle with less than twice its area. [7]

The centers of four squares, all constructed either inside or outside of the sides of a parallelogram, are the vertices of a square. [8th]

If two lines parallel to sides of a parallelogram are constructed simultaneously to form a diagonal, then the parallelograms formed on opposite sides of that diagonal are equal in area. [8th]

The diagonals of a parallelogram divide it into four equal triangles.

Area formula[ edit ]

A parallelogram can be rearranged into a rectangle with the same area.

K = b h {\displaystyle K=bh} Animation for the area formula

All area formulas for general convex quadrilaterals apply to parallelograms. Other formulas are specific to parallelograms:

A parallelogram with base b and height h can be split into a trapezoid and right triangle and converted into a rectangle as shown in the figure on the left. This means that the area of ​​a parallelogram is equal to that of a rectangle with the same base and height:

K = w h . {\displaystyle K=bh.}

The area of ​​the parallelogram is the area of ​​the blue area that represents the interior of the parallelogram

The base-height-area formula can also be derived using the figure on the right. The area K of the parallelogram on the right (the blue area) is the total area of ​​the rectangle minus the area of ​​the two orange triangles. The area of ​​the rectangle is

K rect = ( B + A ) × H {\displaystyle K_{\text{rect}}=(B+A)\times H\,}

and is the area of ​​a single orange triangle

K tri = A 2 × H . {\displaystyle K_{\text{tri}}={\frac {A}{2}}\times H.\,}

Hence the area of ​​the parallelogram

K = K rectangle − 2 × K tri = ( ( B + A ) × H ) − ( A × H ) = B × H . {\displaystyle K=K_{\text{rect}}-2\times K_{\text{tri}}=((B+A)\times H)-(A\times H)=B\times H.}

Another area formula for two sides B and C and angle θ is

K = B ⋅ C ⋅ sin ⁡ θ . {\displaystyle K=B\cdot C\cdot \sin \theta .\,}

The area of ​​a parallelogram with sides B and C (B ≠ C) and the angle at the intersection of the diagonals is given by [9]

K = | Tan ⁡ γ | 2 ⋅ | B2-C2| . {\displaystyle K={\frac {|\tan \gamma |}{2}}\cdot \left|B^{2}-C^{2}\right|.}

If the parallelogram is determined from the lengths B and C of two adjacent sides together with the length D 1 of one of the two diagonals, then the area can be found from Heron’s formula. Concrete it is

K = 2 S ( S − B ) ( S − C ) ( S − D 1 ) {\displaystyle K=2{\sqrt {S(S-B)(S-C)(S-D_{1}))) }

where S = ( B + C + D 1 ) / 2 {\displaystyle S=(B+C+D_{1})/2} and the leading factor 2 comes from the fact that the chosen diagonal divides the parallelogram into two congruent ones Share divides triangles.

Area in terms of Cartesian coordinates of vertices[edit]

Let vectors a , b ∈ R 2 {\displaystyle \mathbf {a} ,\mathbf {b} \in \mathbb {R} ^{2}} and let V = [ a 1 a 2 b 1 b 2 ] ∈ R 2 × 2 {\displaystyle V={\begin{bmatrix}a_{1}&a_{2}\\b_{1}&b_{2}\end{bmatrix}}\in \mathbb {R} ^{2\times 2}} denote the matrix with elements of a and b. Then the area of ​​the parallelogram generated by a and b is | det ( V ) | = | a 1 b 2 – a 2 b 1 | {\displaystyle |\det(V)|=|a_{1}b_{2}-a_{2}b_{1}|\,} .

Let vectors a , b ∈ R n {\displaystyle \mathbf {a} ,\mathbf {b} \in \mathbb {R} ^{n}} and let V = [ a 1 a 2 … a n b 1 b 2 … b n ] ∈ R 2 × n {\displaystyle V={\begin{bmatrix}a_{1}&a_{2}&\dots &a_{n}\\b_{1}&b_{2}&\dots &b_{n}\ end{bmatrix}}\in \mathbb{R}^{2\times n}} . Then the area of ​​the parallelogram generated by a and b is equal to det ( V V T ) {\displaystyle {\sqrt {\det(VV^{\mathrm {T} })}}} .

Let points a , b , c ∈ R 2 {\displaystyle a,b,c\in \mathbb {R} ^{2}} . Then the area of ​​the parallelogram with vertices at a, b, and c is equal to the absolute value of the determinant of a matrix constructed using a, b, and c as rows, with the last column padded with ones, as follows:

K = | det [ a 1 a 2 1 b 1 b 2 1 c 1 c 2 1 ] | . {\displaystyle K=\left|\,\det {\begin{bmatrix}a_{1}&a_{2}&1\\b_{1}&b_{2}&1\\c_{1}&c_{2}&1\ end{bmatrix}}\right|.}

Proof that diagonals bisect[edit]

To prove that the diagonals of a parallelogram bisect, we use congruent triangles:

∠ A B E ≅ ∠ C D E {\displaystyle \angle ABE\cong \angle CDE} (alternative interior angles are equal) ∠ B A E ≅ ∠ D C E {\displaystyle \angle BAE\cong \angle DCE} (alternative interior angles are equal measure).

(since these are angles that a transversal makes with parallel lines AB and DC).

Also, since opposite sides of a parallelogram are equal in length, side AB is equal in length to side DC.

Hence the triangles ABE and CDE are congruent (ASA postulate, two corresponding angles and the included side).

Because of this,

A E = C E {\displaystyle AE=CE} B E = D E . {\displaystyle BE=DE.}

Since the diagonals AC and BD divide into segments of equal length, the diagonals bisect.

Since diagonals AC and BD bisect each other at point E, point E is the midpoint of each diagonal.

Lattice of parallelograms[edit]

Parallelograms can tile the plane by translation. When edges are equal or angles are right, the symmetry of the lattice is higher. These represent the four Bravais lattices in 2 dimensions.

Grid form square rectangle rhombus parallelogram system square

(tetragonal) Rectangular

(orthorhombic) Centered rectangular

(orthorhombic) oblique

(monoclinic) Boundary conditions α=90°, a=b α=90° a=b No symmetry p4m, [4,4], order 8n pmm, [∞,2,∞], order 4n p1, [∞+,2 ,∞+], order 2n form

Parallelograms arising from other figures[ edit ]

Any quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of ​​the quadrilateral, A q , as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral), while that of the small triangle, A s is one Quarters of A l (half linear dimensions give a quarter area), and the area of ​​the parallelogram is A q minus A s . Proof without words of Varignon’s theorem

Automedian triangle[ edit ]

An automedian triangle is one whose medians have the same proportions as its sides (but in a different order). If ABC is an automedian triangle in which the vertex A faces side a, G is the centroid (where the three bisectors of ABC intersect) and AL is one of the extended bisectors of ABC, with L lying on the circumcircle of BGCL is a parallelogram.

Varignon parallelogram [ edit ]

The midpoints of the sides of any quadrilateral are the vertices of a parallelogram called a Varignon parallelogram. If the quadrilateral is convex or concave (i.e., does not intersect itself), then the area of ​​the Varignon parallelogram is half the area of ​​the quadrilateral.

Tangent parallelogram of an ellipse

For an ellipse, two diameters are said to be conjugate if and only if the tangent to the ellipse at one endpoint of one diameter is parallel to the other diameter. Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a boundary parallelogram, formed by the lines tangent to the ellipse at the four extremities of the conjugate diameters. All tangent parallelograms for a given ellipse have the same area.

It is possible to reconstruct an ellipse from any pair of conjugate diameters or from any tangent parallelogram.

Faces of a parallelepiped [ edit ]

A parallelepiped is a three-dimensional figure whose six faces are parallelograms.

See also[edit]

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(4) Likewise, in a quadrilateral, if two angles have no side in common, they are opposite angles. From this we have $\Angle A$ and $\Angle C$ as opposite angles and $\Angle B$ and $\Angle D$ as opposite angles. So there are two pairs of opposite angles.

Hint: The sum of all angles of a quadrilateral is ${360^ \circ }$. If all angles measure ${90^ \circ }$ then the quadrilateral is a rectangle and if all sides are equal then the quadrilateral is square. In a rectangle and parallelogram, opposite sides are parallel and equal. And in the case of a square and a rhombus, opposite sides are parallel and all sides are the same length.

(3) We also know that in a quadrilateral two angles are adjacent if they have a common side. So for the above quadrilateral we have: A). For side $AB$, $\angle A$ and $\angle B$ are adjacent angles.B). For side $BC$, $\angle B$ and $\angle C$ are adjacent angles.C). For side $CD$, $\angle C$ and $\angle D$ are adjacent angles.D). And for the side $DA$, $\Angle D$ and $\Angle A$ are adjacent angles. Thus there are four pairs of adjacent angles.

Full step-by-step answer:

Hint: Draw a polygon, which is a closed figure bounded by straight line segments. Now compare any two sides of the polygon we drew. It can be a triangle, a rectangle or any figure. Compare the adjacent pages. Adjacent sides of a polygon are two lines that meet at the vertex of a polygon. They are usually found in triangles and other polygons. The two sides that meet at a corner point of the polygon are called the adjacent side. This is made clear by the diagram. We can also take an example of another polygon that is a closed figure bounded by a straight line segment. Look at the polygon we drew. The line segments that form a polygon are called its sides. The sides of the given polygon are AB, BC, CD, DE, and EA. For example, consider sides AB and BC. AB has endpoint B and BC has endpoint B. in AB and BC have common endpoint B. Therefore we can call AB and BC neighboring sides of the polygon. Thus, any two pages that share a common endpoint are adjacent pages. The other pair of adjacent sides of the polygon are B and CD, CD and DE, DE and EA, and EA and AB. Similarly, we can take other examples of polygons like triangle, cube, rectangle or any quadrilateral. $\therefore $ Adjacent sides of a polygon are any two sides with a common vertex. $\therefore $ option (C) is the correct answer. Note: Consecutive sides are now two sides of a polygon that share a common angle. We can see consecutive sides in each figure like triangle, rectangle etc. Students should remember 3 properties of polygons. (1) polygon is a closed shape in the plane, (2) the sides of a polygon are line segments, and (3) the sides of a polygon meet only at endpoints.

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Table of Contents

rectangle definition

For a shape to be a rectangle, it must be a four-sided polygon with two pairs of parallel, congruent sides and four interior angles of 90° each. If you have a shape that fits this description, so is all of this:

An airplane figure

A closed form

A square

A parallelogram

The four sides of your polygon must also be two congruent pairs to create two pairs of parallel sides. The base and top are the same length, and the left and right sides are the same length.

Is a rectangle a parallelogram or a rhombus?

A parallelogram and a rhombus can only be rectangles if their interior angles are both 90°.

Is a square a rectangle?

While a rectangle is a type of quadrilateral, parallelogram, closed shape, and plane figure, only a square is always a type of rectangle.

What is a rectangle?

Rectangles are very handy to have around. You see them in bricks, cement blocks, picture frames, posters, sheets of paper, the snapping faces of game pieces, the sides of shoe boxes and cereal boxes, and many other everyday objects.

Rectangles are great because they can be stacked neatly since they have two pairs of parallel sides. Their right angles keep built things (houses, office buildings, schools) standing straight and tall.

You can use four linear (straight) objects to create a rectangle. Make sure two of the objects are the same length and the other two objects are the same length. Arrange them so that the longer pieces are parallel and spaced exactly one distance apart, allowing the other two shorter pieces to touch their ends.

If all four ends touch, you may need to adjust to ensure all four interior angles look like right angles or 90°. Adjacent sides of a rectangle are perpendicular.

Later we will see how to draw a rectangle using a protractor, ruler (or ruler) and pencil.

Properties of rectangles

The most important identifying feature of a rectangle are its four interior right angles. You cannot construct a rectangle unless these four angles add up to 360° and each measure 90°. When you do that, the four sides automatically create the other identifying property.

The other property that identifies rectangles is that opposite sides are congruent and parallel. Congruent means they are the same length; parallel means they are equidistant from each other along their entire length.

A rectangle has no restrictions on the length of its two pairs of sides; You can have a very long, low rectangle, or a very thick rectangle, or a rectangle with four equal sides (that’s a square).

How to construct a rectangle

A protractor measures angles. A ruler (or ruler) makes straight lines. Use the ruler or ruler to draw a straight line segment on a piece of paper, about the bottom third of the sheet. This line segment is your base. Align your protractor with this line segment, working on one endpoint at a time.

At each end of the line segment, mark a 90° angle exactly at the end point. Use the ruler to connect this 90° mark and the endpoint of the line segment. You now have the two sides of the rectangle.

Mark a new endpoint on one of these new sides, some distance from your base. Rotate the protractor 90° and align both sides with the end point of this newly drawn side. Mark 90° with the protractor and again use the ruler to connect the endpoint of the side to this new 90° mark. If this line segment intersects the other side, you have constructed a rectangle.

Of course, if you use a ruler with markings in inches or centimeters, you can measure the length of your base, measure the length of the two left and right sides, and make sure the long top is equal to the length of the base.

Both methods give you a rectangle that you constructed yourself, accurately and quickly.

summary of the lesson

In this lesson, you used the video, drawings, and instructions to learn about rectangles. You’ve learned what a rectangle is, how to recognize a rectangle in the world around you, how the rectangle fits into the quadrilateral family, and the other shape that’s always a rectangle (just the square!).

You also learned two distinctive properties of rectangles: all rectangles have two pairs of congruent, parallel sides; and all rectangles have four interior angles of 90° each.

Finally, you’ve learned to construct your own rectangle using a ruler, protractor, pencil, and paper. You have learned a lot!

Next lesson:

How to find the area of ​​a rectangle

Rectangle is a two-dimensional geometric figure represented by four sides and four corners. A rectangle contains sides where the length of opposite sides is equal and those sides are parallel to each other. The pages share a corner from adjacent pages with a 90° angle between them. So there are four right angles in a rectangle.

Properties of Rectangle

The properties of a rectangle are given below:

It has four edges and four corners known as vertices.

Diagonals of a rectangle bisect each other.

The area of ​​a rectangle is equal to the product of its length and width.

Each vertex has an angle of 90°

Opposite sides of a rectangle are equal and parallel to each other.

The circumference is twice the sum of length and width.

Sum of all interior angles equals 360 degrees

perimeter of a rectangle

The total displacement traveled by traversing the rectangle’s boundary can be called the perimeter. Since both length and width are measured in units of length, circumference is also measured in units of length.

Scope can be denoted by,

Circumference, P=2 (Length + Width)

area of ​​the rectangle

The area covered by a two-dimensional geometric figure in a plane is called the area of ​​a figure. Thus the area of ​​a rectangle is the area enclosed within its boundaries. It is measured in square units. The area is the product of the length and width of the rectangle.

The area can be denoted by,

Area, A = length × width square units

Diagonal of a rectangle formula

Diagonals of each geometric figure connect alternate vertices. The length of the diagonals of a rectangle can be calculated using the following formula, denoted by d,

where, l = length of rectangle w = width of rectangle

rhombus

A rhombus is also known as a four-sided quadrilateral. It is considered as a special case of a parallelogram. A rhombus contains parallel opposite sides and equal opposite angles. A rhombus is also known as a diamond or rhombus diamond. A rhombus contains all sides of a rhombus of equal length. In addition, the diagonals of a rhombus bisect each other at right angles.

properties of a rhombus

A rhombus contains the following properties:

A rhombus contains all equal sides.

Diagonals of a rhombus bisect each other at right angles.

The opposite sides of a rhombus are parallel in nature.

The sum of two adjacent angles in a rhombus is equal to 180°.

. There is no inscribed circle within a rhombus.

There is no circumscribing circle around a rhombus.

The diagonals of a rhombus lead to the formation of four right triangles.

These triangles are congruent to each other.

The opposite angles of a rhombus are equal.

Joining the midpoint of the sides of a rhombus forms a rectangle.

Connecting the midpoints of the half diagonals creates another rhombus.

perimeter of the rhombus

The perimeter of a rhombus is defined as the total length of its borders that make up the figure. It can also be described as the sum total of the lengths of four sides of a rhombus. The perimeter of a rhombus is defined by:

Circumference, P = 4a units, where the diagonals of the rhombus are denoted d 1 & d 2 and “a” is the side.

area of ​​the rhombus

The area of ​​the rhombus is defined as the area enclosed in a two-dimensional plane. The area of ​​a rhombus is equal to the product of the diagonals of the rhombus divided by 2. The area of ​​the rhombus can be defined by the following formula:

Area, A = square units, where d 1 and d 2 are the diagonals of a rhombus.

We can easily see that every rhombus is a parallelogram, but the converse is not true. A square can be considered a special case of a rhombus because it contains four sides of equal length. A square has all right angles. However, not all angles of a rhombus are necessarily right angles. Finally, a rhombus containing right angles can be viewed as a square. Therefore we can say

All rhombuses are parallelograms.

All parallelograms are not rhombuses.

All rhombuses are not squares.

All squares are rhombuses.

Is every rectangle a rhombus?

A rectangle is a geometric figure that does not contain all equal sides. A square is a special case of a rectangle with all sides equal. Because we know that a rhombus has all equal sides. The sets of rectangles and rhombuses only intersect at squares. Therefore the rectangle is not a rhombus.

Why is a rhombus a rectangle?

A rhombus is a special case of a rectangle. Because we know that the diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length. Connecting the midpoints of the sides of a rhombus forms a rectangle.

similar questions

Question 1. Calculate the area of ​​a rectangular frame that is 6 inches long and 3 inches wide.

Solution:

Because we know area of ​​a rectangle = (length × width) square units. Substituting the values, we get the area of ​​the rectangular frame = 6 × 3 = 18 square inches

Question 2. Find the length of the diagonals of a rectangle 12 cm long and 8 cm wide.

Solution:

We know diagonal length, D = ⇒ D = ⇒ D = ⇒ D = √208 ⇒ D = 4√3

Exercise 3. Find the area of ​​a rhombus with the two diagonal lengths d 1 and d 2 of 6 cm and 12 cm, respectively.

Solution:

We have diagonal d 1 = 6 cm diagonal d 2 = 12 cm The area of ​​the rhombus is given by A = square units A = A = A = 36 cm2 Therefore the area of ​​the rhombus = 36 cm2.

Question 4. Difference between rhombus and rectangle?

Solution:

Property Diamond Rectangle Sides Equal Sides. Opposite sides are the same. Diagonals The diagonals bisect at an angle of 90°. Diagonals form right angles in the middle. The diagonals bisect at different angles. One angle is an obtuse angle and the other an acute angle. Diagonals form different angles in the middle – an obtuse angle and an acute angle. Angles Opposite angles are equal. Adjacent angles add up to 180°. Opposite and adjacent angles are equal. An angle formed by the adjacent sides of a rectangle is 90°.

Rhombus has all of its sides equal, but all of its angles are not equal. However, opposite angles are equal.

In a rectangle, all angles are equal, but not all sides are equal. However, the opposite sides are the same.

(4) Likewise, in a quadrilateral, if two angles have no side in common, they are opposite angles. From this we have $\Angle A$ and $\Angle C$ as opposite angles and $\Angle B$ and $\Angle D$ as opposite angles. So there are two pairs of opposite angles.

Hint: The sum of all angles of a quadrilateral is ${360^ \circ }$. If all angles measure ${90^ \circ }$ then the quadrilateral is a rectangle and if all sides are equal then the quadrilateral is square. In a rectangle and parallelogram, opposite sides are parallel and equal. And in the case of a square and a rhombus, opposite sides are parallel and all sides are the same length.

(3) We also know that in a quadrilateral two angles are adjacent if they have a common side. So for the above quadrilateral we have: A). For side $AB$, $\angle A$ and $\angle B$ are adjacent angles.B). For side $BC$, $\angle B$ and $\angle C$ are adjacent angles.C). For side $CD$, $\angle C$ and $\angle D$ are adjacent angles.D). And for the side $DA$, $\Angle D$ and $\Angle A$ are adjacent angles. Thus there are four pairs of adjacent angles.

Decide whether each of these statements is true always, sometimes, or never. Â If it is sometimes true, draw and describe one character that is true and another character that is not.

When using this activity in the classroom, teachers should prioritize Math Practice Standard 6: Pay Attention to Accuracy. Students should base their reasoning on side lengths, side relationships, and angle measurements.

The purpose of this activity is for students to reason about different types of shapes based on their defining attributes and to understand the relationship between different categories of shapes that share some defining attributes. In cases where the list of defining attributes for the first shape is a subset of the defining attributes of the second shape, the statements are always true. In cases where the list of defining attributes for the second form define a subset of the attributes of the first form, then the statements will sometimes be true.

solution

1. A rhombus is a square.

That’s true sometimes. Â It is true if a rhombus has 4 right angles. Â It is not true if a rhombus has no right angles.

Here is an example when a rhombus is a square:

Here is an example when a rhombus is not a square:

2. A triangle is a parallelogram.

That’s never true. Â A triangle is a three-sided figure. Â A parallelogram is a four-sided figure with two sets of parallel sides.

3. A square 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, all squares are parallelograms.

4. A square is a rhombus

This is always true. Â Squares are quadrilaterals with 4 congruent sides. Â Since rhombuses are quadrilaterals with 4 congruent sides, squares are also rhombuses by definition. A

5. A parallelogram is a rectangle.

That’s true sometimes. Â It is true if the parallelogram has 4 right angles. Â It is not true if a parallelogram has no right angles.

Here is an example when a parallelogram is a rectangle:

Here is an example when a parallelogram is not a rectangle:

6. A trapezoid is a quadrilateral.

This is always true. Â Trapezoids must have 4 sides, so they must always be squares.