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As shown in the figure, △ ABC is an equilateral triangle, the bisectors of ∠ ABC and ∠ ACB intersect at O, Bo and Co, and the vertical bisectors of CO intersect at e and F As shown in the figure, △ ABC is an equilateral triangle, the bisectors of ∠ ABC and ∠ ACB intersect at points o, Bo and Co, the vertical bisectors of BC intersect at points E and F, and the perpendicular feet are m and N respectively
Proof: connect OE, of
In the equilateral triangle ABC
The bisectors of ∵ B and ∵ C intersect at O, and the vertical bisectors of OB and OC intersect at e and F,
∴∠OBC=∠OCB=30°,OE=BE,OF=FC．
∴∠OEF=60°,∠OFE=60°．
∴OE=OF=EF．
∴BE=EF=FC．
As shown in the figure, it is known that △ ABC is isosceles right triangle, and EC ⊥ AC is at C, AE = BF. Try to judge the position relationship between AE and BF and explain the reason
AE ⊥ BF. The reasons are as follows: ∵ ABC is isosceles right triangle, ≌ AB = AC, and EC ⊥ AC is in C, ≁ in RT △ ABF and RT △ CAE, AE = bfac = AB, ≌ Abf ≌ CAE (HL), ≌ ABF = ≌ EAC, ≁ EAC + ≁ bad = 90 °, ≁ ABF + ≌ bad = 90 °, ≌ ADB = 180 ° - (≌ ABF + ≌ bad) = 180 ° - 90 ° = 90 °. ≁ AE ⊥ BF
As shown in the figure, △ ABC is an equilateral triangle, points D, e and F are on AB, BC and Ca respectively, and △ ADF ≌ △ CFE
If △ ADF ≌ △ CFE, EF = DF
afd=cef fec+efc=180-60=120
So AFD + EFC = 120, DFE = 180-120 = 60
So if EF = DF, DFE = 60, then △ DEF is an equilateral triangle
As shown in the figure, in the triangle ABC, ad is the bisector of the angle ABC, e is the midpoint of BC, the parallel line passing through e as AC intersects AB at m, and the extension of Ca intersects F
Verification: BM = CF
As shown in the figure, in the triangle ABC, ad is the bisector of angle ABC, e is the midpoint of BC, the parallel line passing through e as ad intersects AB at m, and the extension line of Ca intersects F
The title is wrong
reason:
It is impossible to intersect the extension of CA with F
As shown in the figure, if it is a three view of a geometry, then the geometry is______ ．
As shown in the figure, two of the three views of the geometry are rectangular, and one is a ring, so the geometry is a hollow cylinder
As shown in the figure (unit: cm), calculate the surface area and volume of the geometry formed by the shadow part rotating around ab
According to the meaning of the title, the surface area of the object of revolution is composed of three parts: the bottom, side and half spherical surface of the frustum (3 points) S hemisphere = 8 π, the side of frustum = 35 π, and the bottom of frustum = 25 π. Therefore, the surface area of the object of revolution is 68 π (7 points), which is composed of frustum = 13 × [π × 22 + (π × 22) × (π × 52) + π × 52] × 4 = 52 π, (9 points) V hemisphere = 43 π × 23 × 12 = 163 π (11 points) The volume is v frustum − V hemisphere = 52 π − 163 π = 1403 π & nbsp; (cm3) (12 points)
How to draw the shadow of three-dimensional graphics
Shadow is also layered, relative to the theme, when you want to lay a large area of black and white gray (virtual) is the last line
As shown in the figure, the shadow part in the semicircle with radius r takes the straight line with diameter AB as the axis, rotates one circle to get a geometry, and calculates the volume of the geometry (where ∠ BAC = 30 °)
∵ AB is the diameter, ∵ ACB = 90 °. ∵ Tan ∵ BAC = 33, ∵ sin ∵ BAC = 12, and ∵ sin ∵ BAC = bcab, ab = 2R, ∵ BC = 2R × 12 = R, AC = 3R, CD = 3R2. ∵ V1 = 13 π CD2 (AD + BD) = π 2r3. V2 = 4 π 3r3, ∵ v = v2-v1 = 4 π 3r3 − π 2r3 = 56 π R3
The shadow of the right figure is a right angle trapezoid. If you rotate it around the axis Mn, what is the volume of the solid figure?
Calculation of column formula
3.14 × 2 × 2 = 12.56 6-3 = 312.56 × 3 = 37.68 37.68 △ 3 = 12.56 -------- 3.14 × 4 = 12.5612.56 × 3 = 37.68 -------- 12.56 + 37.68 = 50.24 -------- idea: first
The following figures are not axisymmetric:
A: A right triangle with an angle equal to 45 degrees
B: A triangle with two angles equal to 37 ° and 106 ° respectively
C: A triangle with two equal angles
D: A right triangle with an angle of 36 degrees
(urgent!)
The first three are isosceles triangles
It's axisymmetric
So choose D: there is a right triangle with an angle of 36 degrees
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