As shown in the figure, in the isosceles trapezoid ABCD, ad ∥ BC, points m and N are the midpoint of AD and BC respectively, and points E and F are the midpoint of BM and cm respectively. (1) prove that the quadrilateral menf is a diamond; (2) when the quadrilateral menf is a square, prove that the height of the isosceles trapezoid ABCD is half of the bottom BC

As shown in the figure, in the isosceles trapezoid ABCD, ad ∥ BC, points m and N are the midpoint of AD and BC respectively, and points E and F are the midpoint of BM and cm respectively. (1) prove that the quadrilateral menf is a diamond; (2) when the quadrilateral menf is a square, prove that the height of the isosceles trapezoid ABCD is half of the bottom BC

(1) In △ ABM and △ DCM, am = DM, a = DAB = DC, ABM ≌ DCM (SAS), BM = cm, e, F and N are the midpoint of BM, cm and BC, respectively, en = 12cm, FN = 12bm, me = 12bm, MF = 12cm, en = FN = FM = em, menf is a rhombus. (2) connecting Mn, ∵ BM = cm, BN = CN, ∵ Mn ⊥ BC, ∵ ad ∥ BC, ∵ Mn ⊥ ad, ∵ Mn is the height of trapezoid ABCD, and ∵ quadrilateral menf is a square, ∵ BMC is a right triangle, and ∵ n is the midpoint of BC, ∵ Mn = 12bc, that is, the height of isosceles trapezoid ABCD is half of the bottom BC

If a is quadratic - a = 5, then - 5A is quadratic + 5a-6=

-5A quadratic + 5a-6=
=-5(a²-a)-6
∴a²-a=5
The original formula = - 25-6
=-31

Given that f (1,0), M is on the x-axis, P is on the y-axis, and Mn = 2MP, PM is perpendicular to PF, when P moves on the y-axis, the trajectory equation of n is obtained

y²=4x

The following equations are transformed into the form of expressing another unknown with an algebraic expression containing one unknown
3x-5t = 1 / 3, y + 1 / 4 =. X + 2 / 4

∵ 3x-5t = 1 / 3 ∵ 9x-15t = 1 ∵ x = (1 + 15t) / 9t = (9x-1) / 15
∵ y + 1 of 4 =. X + 2 ∵ y + 4 = 2x + 8 ∵ y = 2x + 4, x = (y-4) / 2

If the volume of triangular prism abc-a1b1c1 is V, and points P and Q are the midpoint of Aa1 and CC1 respectively, then the volume of pyramid b-apqc is?

Take the midpoint r of BB1, Obviously, the volume of b-rpq is equal to the volume of q-abc (two triangles are congruent), and the volume of q-bpr is equal to the volume of q-abp (equal base and same height), while b-apqc is the combination of q-abc and q-abp, and abc-prq is the combination of b-apqc and b-rpq So the volume of b-apqc is 2 / 3 of that of abc-prq, and obviously the volume of abc-prq is 1 / 2 of that of abc-a1b1c1, so the volume of b-apqc is 1 / 3 of that of abc-a1b1c1, that is v / 3

List the squares of 1-21
It's good to write
For example: the square of 1 =
.
This question is not too difficult,
(answer first, accept first)

1²=1
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
9²=81
10²=100
11²=121
12²=144
13²=169
14²=196
15²=225
16²=216
17²=289
18²=324
19²=361
20²=400
21²=441

The factorization of polynomial m ^ 2 (X-Y) + m (Y-X) is equal to

m^2(x-y)+m(y-x)
=m²(x-y)－m(x-y)
=m(x-y)(m－1)

Given: a + a 1 / 2 = 2, find the value of a & # 178; + A & # 178; 1 / 2

A & # 178; + A & # 178; 1 / 2
=(a + 1 / a) & # - 2
=2²-2
=2

It is known that the perimeter of a parallelogram is 45cm, and the distances between two groups of opposite sides are 4cm and 5cm respectively. The area of the parallelogram is calculated
I'm in a hurry. Come on

Because the distance between the two opposite sides is 4cm and 5cm respectively
So its height is 4cm and 5cm
Let one side of a parallelogram be x (CM), and the height of this side be 4cm,
Then the edge adjacent to it is equal to 22.5-x (CM)
Because the area of the parallelogram = base × height
So we get the equation:
4X＝5（22.5－X）
Solution
X＝12.5
So parallelogram area
＝4X
= 50 (cm2)

The solution equation: (1) 9-10x = 10-9x