Four planes intersect two. How to prove that their intersection lines are parallel

Four planes intersect two. How to prove that their intersection lines are parallel

Counter evidence
Suppose that the intersection lines of a and B on the C plane are l and m respectively, and the two lines are not parallel
Then the two intersecting lines must intersect on this plane
Then we can get that plane a and plane B must intersect
It doesn't correspond to the intersection of two faces
So the two intersecting lines on one side must be parallel
By analogy, four intersecting lines are parallel to each other

It is proved that if two planes intersect the third plane at the same time, their intersection lines are parallel
It's about proving axioms
The teacher asked us to prove it

How can I remember it's axiom without proof
Axioms can't be proved. For example, two parallel lines will never intersect
Theorem is provable and derived from Axiom. For example, two straight lines are parallel, the internal angle is staggered, and the angle of apposition is equal

If non-zero real numbers a, B (a ≠ b) satisfy a2-a + 2007 = 0, b2-b + 2007 = 0, then: 1A + 1b=______ ．

∵ if non-zero real numbers a, B (a ≠ b) satisfy a2-a + 2007 = 0, ①, b2-b + 2007 = 0, ②, ① - ②, then (a-b) (a + B-1) = 0, ∵ a ≠ B, ∵ a + B = 1, ① + ② (a + B) 2-2ab - (a + b) + 4014 = 0, ∵ a + B = 1, ab = 2007, ∵ 1A + 1b = a + bab = 12007

What is the quotient of the sum of 3 / 7 and its reciprocal divided by 1 / 9 of 36?

29/42

What's the rule for merging like items?

A term with the same letter and the same exponent of the same letter is called a similar term. Merging the similar terms in a polynomial into one term is called merging the similar terms. When merging, the coefficients are added, and the letter and the exponent of the letter remain unchanged
This is the rule of merging the same kind

For a bottle of alcohol, first pour out 1 / 3, then pour back 40g, the second pour out the remaining 5 / 9, and the third pour out 180g. At this time, there is still 50g left in the bottle,
How many grams of alcohol are there in the bottle?

Let's set the original alcohol x G
[x*(1-1/3)+40]*(1-5/9)-180=50
x=716.25g

Please divide 9 out of 8 into 11 out of 9

9/8,11/9
81/72,88/72

X divided by five sixths is four fifths
How to solve the equation

X ÷ 5/6 = 4/5
X = 4/5 × 5/6
X = 2 / 3 two thirds

No matter what the value of K is, the point that the image of quadratic function y = x2 + (2-k) x + K always passes through is

Quadratic function y = x ^ 2 + (2-k) x + k
Y=X^2+2X-KX+K=X^2+2X-K(X-1)
When x = 1, K does not affect the value of Y
Because when x = 1, y = 3
So no matter what the value of K is, the image of quadratic function y = x2 + (2-k) x + K always passes through (1,3)

From 1 to 50, find 5 numbers whose reciprocal sum equals 1?

1/2 + 1/4 + 1/8 + 1/12 + 1/24 = 1
The five numbers are: 2, 4, 8, 12, 24