Three planes intersect each other. A, B and C are three intersecting lines. If a intersects B and P, prove that ABC three lines are at the same point

Three planes intersect each other. A, B and C are three intersecting lines. If a intersects B and P, prove that ABC three lines are at the same point

a=A∩B,b=B∩C,c=C∩A,P=a∩b；
P ∈ a, a ∈ a, so p ∈ a; P ∈ B, B ∈ C, so p ∈ C;
So p ∈ C ∩ a, that is p ∈ C;
So the three lines a, B and C are in common with P

If plane a intersects plane B and plane C, what are the intersection lines of these three planes

The meaning of the title is not very clear
If every two planes intersect, the answer is one or three
If a and B, a and C intersect respectively, then the answer is three (B and C are not parallel) or two (B and C are parallel) or one (three planes intersect on a line)

Given that plane α ∩ plane β = a, plane β ∩ plane γ = B, plane γ ∩ plane α = C, the intersection of ABC and the same point is proved

Because a is in β, B is in β, so a / / B, or a, B intersect. When a, B intersect, let p be the intersection point, because P is on a, a is in plane α, so p is in α, because P is on B, B is in plane y, so p is in Y, that is, P is a common point of plane α and plane y, so p is on the intersection line C of plane α and plane y, that is, a, B, C phase

If three planes intersect each other, how many intersecting lines are there?

One (three planes intersect in a straight line) or three (two intersect each other)

There are several intersecting lines when three planes intersect each other

Three or one

Three planes intersect each other on three intersecting lines. It is proved that these three intersecting lines are parallel or intersect at a point

Three straight lines are obtained when three planes intersect each other. Prove that the three straight lines intersect at the same point or are parallel. It is known that: plane α ∩ plane β = a, plane β ∩ plane γ = B, plane γ ∩ plane α = C. prove that a, B, C intersect at the same point, or a ∩ B ∥ C. prove that: ∩ α ∩ β = a, β ∩ γ = B ∩ a, B β ∩ a, B intersect or a ∥ B

If three planes intersect each other and the intersecting lines do not coincide, how to prove that the intersecting lines are at one point or parallel

Three planes intersect each other to get three straight lines. Verification: the three straight lines intersect at the same point or are parallel
It is known that plane α ∩ plane β = a, plane β ∩ plane γ = B, plane γ ∩ plane α = C
Verification: A, B, C intersect at the same point, or a ‖ B ‖ C
It is proved that: α ∩ β = a, β ∩ γ = B
∴a,bβ
A, B intersect or a ‖ B
(1) When a and B intersect, let a ∩ B = P, that is, P ∈ a, P ∈ B
And a, B β, a α
Therefore, P is the common point of α and β
And ∩ α ∩ γ = C
Know P ∈ C from Axiom 2
A, B and C all pass through point P, that is, a, B and C are three lines in common
(2) When a ‖ B
∩ γ = C and a α, a γ
∥ a ∥ C and a ∥ B
∴a‖b‖c
So a, B and C are parallel
It can be seen that a, B and C intersect at one point or are parallel
Note: this conclusion is often used as a theorem and is often used in judging problems

Proof: the three planes intersect each other, and the intersecting lines are parallel or intersecting

It is proved that: let plane a ∩ β = straight line a, β ∩ γ = B, γ ∩ α = C, and a ∩ 449; B, because a ∩ 449; B, B is in plane γ, so a ∩ 449; γ (lines parallel, lines parallel) α crosses straight line a, a ∩ 449; γ and γ ∩ α = C, so a ∩ 449; C (lines parallel, lines parallel) so a ∩ 449

If a line is parallel to two intersecting planes at the same time, how can we prove that the line is parallel to the intersecting line?

A parallel plane a
A parallel plane B
A = b = C
Then a is parallel to C
This is a theorem

If two intersecting planes pass through one of the two parallel lines respectively, the position relationship between their intersecting lines and the two parallel lines is ()
A. All parallel B. all intersecting C. one intersecting, one parallel D. all different faces

As shown in the figure: it is known that: α ∩ β = m, a ∩ B, a ⊂ α, B ⊂ β. Then a ∥ B ∥ m. It is proved that: ∩ a ∩ β = m, B ⊂ β, B ⊂ m.. A ∥ B ∥ M can be determined by ∩ a ∩ β