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Take a point G on the extension line of one side of the square ABCD and connect it with a, intersect BC at point F, connect diagonal BD and intersect AF at point E. AE = 5, AF = 3 are known, and calculate the length of FG chart
Let ad be 1, because the triangle AED and Feb are similar, we can get AD / BF = AE / EF, BF = 3 / 5, so CF = 2 / 5. Let GF = x, Ag / FG = ad / FC
FG = 16 / 3 = 5 and 1 / 3
In the parallelogram ABCD, the crossing point B is be ⊥ CD, the perpendicular foot is e, connecting AE, and F is the upper point of AE, and ∠ BFE = ∠ C
(1) Verification: Δ Abf ∽ Δ ead;
(2) If AB = 8, ∠ BAE = 30 degrees, calculate the length of AE;
(3) Under the conditions of (1) and (2), if ad = 6,
Finding the length of BF
(1) Because the row quadrilateral ABCD,
Therefore, D + C = 180 degree
Because ∠ AFB + ∠ BFE = 180 ° and ∠ BFE = ∠ C
Therefore, d = AFB;
Because AB / / ed
Therefore, BAF = AED
So Δ Abf ∽ Δ EAD
(2) In the right triangle BAE, ab = 8, ∠ BAE = 30 degree
AB / AE = cos30 ° = (radical 3) / 2
8 / AE = (radical 3) / 2
So AE = 16 (radical 3) / 3
(3) Because Δ Abf ∽ Δ EAD
So AE / AB = ad / BF
[16 (radical 3) / 3] / 8 = 6 / BF
So BF = 3 (root 3)
It is known that in the parallelogram ABCD, B acts as be ⊥ CD to e, connects AE, f is the point on AE, and ∠ BFE = ∠ C
① Verification: △ Abf ∽ EAD
② If AB = 4, ∠ EAB = 30 °, find the length of AE
③ Under the condition of (1) and (2), if ad = 3, find the length of BF
A B
F
D E C
① Because ABCD is a parallelogram, ∠ BAE = ∠ AED, ∠ bad = ∠ C
And because ∠ BFE = ∠ C,
So ∠ bad = ∠ C = ∠ BFE = ∠ BAF + ∠ ABF = ∠ DAE + ∠ BAF,
So ∠ DAE = ∠ ABF,
So △ Abf ∽ ead (three equal angles)
② For △ Abe, 1 / 2Ab * abtan30 degree = 1 / 2ae * absin30 degree (the area of the same triangle is equal),
So AE = 8 / 3 times root 3
③ Because △ Abf ∽ ead,
So AB / AE = BF / AD,
So BF = 3 / 2 times root 3
In the rectangular coordinate system, a (0,1), B (0,2), C (2,2), D (2,1) rotate the quadrilateral ABCD around the straight line y = 1 to obtain the volume of the geometry
This is a cylinder, the radius of the bottom is ab = CD = 1, the height is h = 2, so the volume formula of the cylinder is v = 2 π R & # 178; H = 2 × π × 1 & # 178; x 2 = 4 π,
In the quadrilateral ABCD, if a (0,0), B (1,0), C (2,1), D (0,3) rotate around the y-axis for one circle, the volume of the rotator is______ ．
If the quadrilateral ABCD rotates around the y-axis for one circle, the upper part of the rotator is a cone, and the lower part is an inverted frustum. Therefore, V-cone = 13 π r2h = 13 π × 22 × 2 = 83 π, V frustum = 13 π H (R2 + R2 + RR) = 13 π × 1 × (22 + 12 + 2 × 1) = 73 π, v = V-cone + V frustum = 5 π
In the quadrilateral ABCD, ∠ ADC = ∠ B = 90 ° de ⊥ AB, the perpendicular foot is e, ad = CD, and de = be = 5, please use the method of rotating graphics to find the area of quadrilateral ABCD
Rotate RT △ DEA 90 ° anticlockwise around D, as shown in the figure. ∵ rotation does not change the shape and size of the figure, ∵ a coincides with C, ∵ a = ∵ DCE ′, ∵ e ′ = ∵ AED = 90 °. In quadrilateral ABCD, ∵ ADC = ? B = 90 ° and ∵ a + ∵ DCB = 180 °;, ? DCE ′ + ? DCB = 180 °, i.e. points B, C, e
In the quadrilateral ABCD, ∠ ADC = ∠ e = 900, DB ⊥ AE, the perpendicular foot is B, and DB = EB = 5, please use the method of rotating graphics to calculate the area of quadrilateral AECD
As shown in the figure, ∠ BAC = 90 ° and △ ABC rotates counterclockwise around point a to get △ ade, just point D is on BC, connecting CE. (1) what's the relationship between ∠ BAE and ∠ DAC? Explain the reason; (2) what's the relationship between △ abd and △ ace? Explain the reason; (3) what's the relationship between BC and CE? Why
As shown in the figure, there is a quadrilateral ABCD, the known angle a = angle c = 90 degree angle d = 45 degree AB = 4cm CD = 8cm, find the area of this figure
If the quadrilateral is divided into two parts, it is a triangle on the top and a trapezoid on the bottom, and then it is combined
Extend the extension line of CB to DA at E
∵∠D＝45, ∠C＝90
∴∠E＝45
∴CE＝CD＝8
∴S△DCE＝CD²/2＝32
S△ABE＝AB²/2＝8
∴SABCD＝S△DCE-S△ABE＝32-8＝24
The math tutor group has answered your question. Please accept it as the best answer
Given the quadrilateral ABCD, make the symmetric figure of quadrilateral ABCD about point o
Connect AO and extend a 'so that OA' = OA, and make points B ', C', d ',
Connect a'b'c'd'to get the symmetry figure
Given four points a (0,1) B (- 3,4) C (- 5,4) d (- 5,1); (1) draw a symmetric graph a'b'c'd 'of quadrilateral ABCD with respect to x = - 1; (2) you
A(-2,1)B(1,4)C(3,4)D(3,1)
Each point y is constant
X becomes - X-2
(2) I didn't ask
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