In triangular pyramid a-bcd, ab ⊥ CD, AC ⊥ BD, then the projection of point a in plane BCD is △ BCD A. Center of gravity

In triangular pyramid a-bcd, ab ⊥ CD, AC ⊥ BD, then the projection of point a in plane BCD is △ BCD A. Center of gravity

Choose C. Center
Let the projection of point a in plane BCD be o, then
OB is the projection of AB in plane BCD,
∵AB⊥CD
According to the inverse theorem of the three perpendicular theorem: CD ⊥ ob
Similarly, BD ⊥ OC can be proved
O is the perpendicular of △ BCD

In the triangular prism abc-a1b1c1, ab ⊥ AC, the projection of vertex A1 on the ground ABC is exactly point B, and ab = AC = A1B = 2. It is proved that plane a1ac ⊥ plane ab1b

Certification:
∵ AC⊥AB ,A1B1//AB
∴ AC⊥A1B1（1）
The projection of vertex A1 on the ground ABC is exactly point B
Ψ A1B ⊥ plane ABC
∴ A1B⊥AC （2）
From (1) (2)
AC ⊥ plane ab1b
And ∵ AC is in plane a1ac
Plane a1ac ⊥ plane ab1b

In the triangular prism abc-a1b1c1, ab ⊥ AC, the projection of vertex A1 on the bottom ABC is just the help of the great God for point B
And ab = AC = A1B = 2. (1) find the angle between edge Aa1 and BC; (2) take the midpoint P of line b1c1 to find the tangent of dihedral angle p-ab-a1

(2) As shown in the figure, if a is taken as the origin to establish the space rectangular coordinate system, then C (2,0,0), B (02,0), a 1 (0,2,2), B 1 (0,4,2), so Aa1 = (0,2,2), BC = b1c1 = (2, - 2,0). So cos < Aa1, BC > = Aa1, BC | Aa1 | BC | = - 1,2

If every vertex of a cube of 8 is on a sphere, the volume of the sphere is

Because the cube volume = side length ^ 3 = 8, the side length is 8, and the root of the third power is 2
Connect the diagonals of one face of the cube. The length of the diagonals can be calculated as 2 √ 2. Connect the vertices of the cube from the center of the circle. The diameter of the ball ^ 2 = the diagonal of the face ^ 2 + the side length ^ 2 can be obtained
=(2√2)^2+2^2
=8+4
=12
So we can find the diameter of the ball = √ 12 = 2 √ 3
So the radius of the ball is 2 √ 3 / 2 = √ 3
So the volume of the sphere is 4 π R ^ 3 / 3
=4*3.14*(√3)^3/3
=21.76
A: the volume of the ball is about 21.76

Who can tell me all the words, Pinyin and explanations in the first volume of seventh grade Chinese

Words: Fantasy Pinyin: Q í Hu à n: fantastic and illusory reverie, strange and changeable scenery fantasy words: Ancient Pinyin: Yuan Gu (far in the U on the table 3, ancient is in the U on the table 2) ancient times refers to the long historical period from the emergence of human beings to the formation of the country (from about 1.7 million years ago to 2070 BC

Explanation and Pinyin of the words behind "footprints on the moon" in Lesson 18 of seventh grade Chinese Book Volume I

It takes less manpower and material resources to harvest more sea area. It refers to a certain range of the ocean. It talks freely about Shenwang and yearns for a milestone in the heart

Vocabulary explanation and Pinyin

9：
Persistence: persistence
Spur: to drive a horse with a whip or a spur
Fame: a great reputation
Reward: do certain things and get certain thanks
High hopes: high hopes
Trample: to trample, insult, or invade with violence
Reprimand: reprimand
Chagrin: a great annoyance
Intoxication: I am addicted to seeing you
Intoxication: very intoxicated and see things
Sudden death: sudden death
A clear conscience: it means to be worthy of others and not feel ashamed

Pinyin for word explanation after class 16-18, Grade 7
Pinyin should have all

16 fossil songs
Fantasy: strange and illusory
Ancient times: remote ancient times
Skeletons: human bones. In the text, they generally refer to animal bones
Nonexistence: nonexistence
Stealth: a secret walk
To contain or contain
Verdant: (vegetation) lush
Elegant: quiet and elegant
Admiration: praise and admiration
Creator: Christians believe that God creates all things, so they call him creator
Dry sea and rotten stone: dry sea and rotten stone, usually refer to a very long time
Solar rotation and star shift: the direction of the sun's rotation, the position of the stars, and the change of time
That's all I know

Help explain the words in Volume 1 of Grade 7
Words that need to be explained: wishful thinking, condensation and noise

Analysis: 1. Dull thinking. 2. Fantasy. Rich imagination in literary creation. 3. Unrealistic, hard to achieve ideas. 4. Feel very envious of what you can't get. Deeply immersed in a reverie, describe a person dull thinking about a thing. For example: in the other side of the mountain: I often fall in the window crazy. 1

As shown in the figure, in the triangle ABC, BD ⊥ AC ∠ a = 50 °∠ CBD = 25 ° if AC = 5, then AB is equal to cm

∵BD⊥AC,∠CBD=25°,∴∠C=65°,
If a is used as AE ⊥ BC, then ∠ CAE = 90 ° - C = 25 °,
∵∠A=50°,
∴∠BAE=25°,
In Δ AEB and Δ AEC,
∠CAE=∠BAE=25°,
∠AEB=∠AEC,
AE=AE,
∴ΔAEB≌ΔAEC(ASA),
∴AB=AC=5.