There is a point a on the x-axis and a point B C (2,1) on the line y = X

There is a point a on the x-axis and a point B C (2,1) on the line y = X

Take the symmetry point m (2, - 1) of point c about the x-axis. From the symmetry, it can be seen that am = AC
Let C be the symmetry axis n (1,2) of y = X. similarly, BN = BC
So ABC circumference = AB + AC + BC = AB + am + BN = ma + AB + BN
In this case, the circumference of ABC is equal to the distance from m to n via the x-axis and the two moving points on y = X
From the shortest line between two points, we can know that the shortest circumference of ABC is the distance of straight line Mn
At this time, a and B are the intersection points of Mn and X axis y = x respectively
The Mn equation is y = 5-3x
Intersection of x-axis with a (5 / 3,0) and y = x with B (5 / 4,5 / 4)

The perimeter of triangle ABC is 1. Connect the midpoint of each side to form the second triangle, and then connect the midpoint of the second triangle
And so on
The perimeter of the 2005 triangle is ()
A 1/2004
B 1/2005
C 1 / 2 ^ 2004 (1 / 2004 of 2)
D 1/2^2005

The perimeter of the second is 1 / 2 of that of the first
.
The circumference of the nth is the first: 1 / 2 ^ (n-1)
So the 2005 circumference is 1 / 2 ^ 2004
C

It is known that the perimeter of △ ABC is 1. Connect the midpoint of three sides of △ ABC to form the second triangle, then connect the midpoint of three sides of the second triangle to form the third triangle, and so on. The perimeter of the third triangle is______ ．

The ratio of the three sides of the new triangle to the three sides of the original triangle is 1:2, they are similar, and the similarity ratio is 1:2, and so on: the similarity ratio of the 2006 triangle to the original triangle is 1:22005, and the perimeter of the 2006 triangle is 122005

It is known that the perimeter of △ ABC is 1. Connect the midpoint of three sides of △ ABC to form the second triangle, then connect the midpoint of three sides of the second triangle to form the third triangle, and so on. The perimeter of the third triangle is______ ．

The ratio of the three sides of the new triangle to the three sides of the original triangle is 1:2, they are similar, and the similarity ratio is 1:2, and so on: the similarity ratio of the 2006 triangle to the original triangle is 1:22005, and the perimeter of the 2006 triangle is 122005

As shown in the figure, ab = AC, ∠ BAC = 120 ° in △ ABC, ad ⊥ AC intersects BC at point D, and BC = 3aD

It is proved that in △ ABC, ∵ AB = AC, ∵ BAC = 120 °, and ∵ ad ⊥ AC, ∵ DAC = 90 °, and ∵ C = 30 °, CD = 2ad, ∵ bad = ∵ B = 30 °, ad = dB, ∵ BC = CD + BD = AD + DC = AD + 2ad = 3aD

As shown in the figure, in the triangle ABC, the angle c = 90 ° and the points D and E are on AB and AC respectively, and ad × AB = AE × AC.ED Is it perpendicular to ab? Please explain why

Because ad × AB = AE × AC
So ad / AC = AE / AB
And because angle a = angle a
So triangle ABC ∽ triangle AED (∽ means similar)
So angle ade = angle c = 90 degrees
So Ed is perpendicular to ab

In known triangle ABC, angle c = 90 degrees, de are AB.AC And ad * AB = AE, and ED is perpendicular to ab

If ED is perpendicular to AB, then ad / AC = AE / ab
AE=AD*AB/AC
The condition given by the landlord is ad * AB = AE
According to the known conditions, it is impossible to deduce AC = 1
So it is estimated that the building owner mistakenly wrote ad * AB = AE * AC as ad * AB = AE
If so, the similarity of triangles can be proved by the fact that the two adjacent sides are proportional and the angle a is the same
Angle EDA = angle c = 90 degrees, i.e. ED is perpendicular to ab

In △ ABC, AE bisection ∠ BAC intersects BC with E, de ‖ AC intersects AB with D, and DF ‖ BC intersects AC with F

It is proved that: as shown in the figure, ∵ AE bisection ∵ BAC intersects BC with E, ∵ de ∥ AC, ∵ de ∥ 2 = ∥ 3, ∵ 1 = ∥ 3, ∵ ad = de. and ∵ de ∥ AC, DF ∥ BC,