If it is a rectangle, it is a square If it is a diamond, then it is a square

If a rectangle (two adjacent sides are equal), it is a square; If a diamond (with one corner is a right angle), then it is square.

If a parallelogram is diagonal (perpendicular and equal), then it is square.

If the side length of the square is a, then its diagonal length is ((root number2)a), and the area is (a 2)The diagonal length of the square is a, then its side length is ((root number2 2)a), and the area is (a 2 2).

If the area of a square is 10 cm 2, then its diagonal length is ((root number 20) cm 2) and the side length is ((root number 10) cm 2).

1. If a rectangle is equal on opposite sides then it is a square; If a diamond has an angle of 90 degrees, then it is square.

If the diagonal lines of a parallelogram are equal and bisected from each other, then it is a square.

2,(1),a root number 2; a^2

2), root number 2 a; 2a^2

3), root number 5; Root number 10

1. If the diagonal lines of a parallelogram (equal and perpendicular to each other) are square.

2.If the side length of a square is a, then its diagonal length is (a twice the root number) and the area (the square of a).

If the diagonal length of a square is a, then its side length is (2 times the root number of 2 times a) and the area is (1/2 times the square of a).

If the area of a square is 10 cm 2, then its diagonal length is (2 times the root number 5) and the side length is (root number 10).

The degree can be obtained by proving that the two times Hahashi Tong congruence can be obtained, and the sedan car is as shown in the following figure

Junior high school mathematics, geometric figure folding problems are a kind of graphic problems that we often encounter in learning, today I will continue to share a few folding problems with you, I hope that the study of these questions will allow you to master the problem-solving skills of this kind of problem faster.

Solution: af=ad=bc=10cm

And ab=6cm

By the Pythagorean theorem.

It can be obtained. BF = 6 cm, while CF = BC-BF = 4 cm

Let ce=m and de=cd-ce=ab-ce=8-m

de=ef

ef=8-m

From the Pythagorean theorem, it can be derived.

ef2=ec2+fc2

i.e. (8-m)2=m2+16

m=3ce is 3cm long

Example Li Naier: As shown in the figure, in the rectangular piece of paper ABCD, AB=4cm, BC=8cm, now A, C coincide, so that the paper is folded and flattened, the crease is EF, and the length of DF is found; Find the area of the AEF of the heavy fiber lifting part; Find the length of the crease ef.

Solution: When df=m, d'f=df=m

And af=ad-af=8-m

ad'=cd=ab=4

From the Pythagorean theorem, it can be derived.

d'a2+d'e2=af2

i.e. (8-m)2=m2+16

m=3, that is, the length of df is 3cm

df = 3cm, then af = ad-df = 5 cm

If you pass the point e as eg ad in g, then eg=ab=4cm

s△aef=1/2*af*eg=10

Pass point F as FH BC at point H.

fh=ab=4cm

eh=bh-be=af-be

And be=df=3cm

eh=2cm

ef2=eh2+fh2

ef=2√5

We can conclude that the square will be along the be'folded in half, point C will fall on A'Dot.

a'be'=∠a'be'

The square diagonal is the bisector of the square angle.

a'bc=∠a'be'+∠a'be'=45°

a'be'=∠a'be'=

a'e'b=∠ce'b=

Again'e'=ce'

e'a'c=∠e'ca'=

Again'a'c+∠ca'b=90°

ba'c=I'll share it with you today, for folding problems, the idea of solving the problem is mainly through right triangles.

The Pythagorean theorem and the investigation of the graph symmetry problem, master these two knowledge points, and apply them flexibly, then the folding problem will be solved.

2.The rectangle should be a square, because if you keep 1 2 unchanged and pull the rectangle up or to the right, it will inevitably cause the state to take 3 to change, so you should default to the square. 3.

The key to solving the problem is to use the vertex in the lower left corner as the middle book to touch the heart, rotate a right triangle in the diagram, and splice it with another to make a 23° angle and a 22° angle to get a 45° angle, see the follow-up answer.

The quadrilateral ABCD is rectangular, DAB=90°, and the parallelogram ABCD is the square of the Zhengbu Bridge

So the answer is: square

Rectangles, diamonds, and squares all have the property of bisecting each other diagonally.

1.Properties of rectangles:

has all the properties of a parallelogram;

The four corners of the rectangle are all right angles;

The diagonal lines of the rectangle are equal;

A rectangle is an axisymmetric figure, and it has two axes of symmetry;

The middle line on the hypotenuse of a right triangle is equal to half of the hypotenuse.

Determination of rectangle: if there is an inner angle that is straight, then the parallelogram of the angle quarrel chain is a rectangle; A parallelogram with equal diagonals is a rectangle; There are three corners that are right angles, and the quadrilateral is rectangular; There are also quadrilaterals with equal diagonals and bisects that are rectangular.

2.Properties of the rhombus:

has all the properties of a parallelogram;

The four sides of the rhombus are all equal;

The two diagonals of the diamond are perpendicular to each other, and each diagonal is bisected by a set of diagonals;

The rhombus is an axisymmetric figure, and the line where each diagonal line is located is its axis of symmetry;

The area of the rhombus is half of the diagonal product.

The method of determining the rhombus: there is a group of parallelograms with equal adjacent sides that are rhombuses; A parallelogram with diagonal perpendicular to each other is a rhombus; All four sides are equal, and the quadrilateral is a rhombus; A quadrilateral with a perpendicular bisection of the angular line is a diamond.

3.The nature of the square: The square has all the properties of a parallelogram, a rectangle, a rhombus.

Edges: The four sides are equal, and the opposite sides are parallel;

Angles: All four corners are right angles;

Diagonals: bisected from each other; Equal; and vertically; Each diagonal is divided into a set of diagonals, that is, the angle between the diagonal line and the side of the square is 45 degrees;

A square is an axisymmetric figure with four axes of symmetry.

The Shengtansun judgment of the square: a feature of the diamond + rectangle; Parallelogram + one right angle + a set of adjacent edges equal.

Method 1: Take the midpoint of the four sides of the rectangle and connect the midpoint to form a diamond.

Method 2: Let the rectangle be ABCD, take a point E on the edge of AB, take E as the center of the circle, AE as the radius to make a circle, and cross CD to F;

Then take F as the center of the circle, EF as the radius to make a circle, cross CD to G, and AEFG to form a diamond.

make the midpoints of the four sides of the rectangle a1b1c1d1 e1, f1, g1, h1;

Connecting the quadrilateral e1f1, e1f1, g1f1, g1h1 quadrilateral e1f1g1h1 is a diamond

Take a little e2 on b2c2 so that e2c2 a2e2 and e2 does not coincide with b2;

Draw an arc with a2 as the center of the circle and a2e2 as the radius, and cross a2d2 to h2;

Draw an arc with e2 as the center of the circle and a2e2 as the radius, and cross b2c2 to f2;

If H2F2 is connected, the quadrilateral a2e2f2h2 is a diamond

--- intersection is the meaning of the logical link word "again".

Rhombus hollow, with equal sides;

rectangular shape, with internal angles of 90 degrees;

Therefore, if the four sides are equal and the inner angles are 90 degrees, the rising quadrilateral is a blind square--- which is the definition, so there is no doubt.

x|x is a square} a=, the geometric feature of its elements is a parallelogram with a large rubber fiber at right angles, b=, the geometric feature of its elements is a parallelogram with equal adjacent sides, by the nature of the intersection, a such as taking the characteristics of the elements in b is that there is a parallelism with a right angle and equal adjacent edges.

If a quadrilateral is both a diamond and a rectangle, then it must be ( square ).

Explanation: The diamond shape has four equal sides. A rectangle with equal sides is a square.

The triangle where <1 is located is an equilateral triangle <1=60 degrees.

The triangle where 2 is located has an isosceles triangle with an angle of 30 degrees, <2=75 degrees.

3. 360 degrees using symmetry and circumference <3=150 degrees.