In the isosceles triangle ABC, the angle c = 90 ° and BC = 3cm, if the center point O of AC is taken as the rotation center Rotate the triangle 180 ° and point B falls at B1. How many centimeters has point B changed from the original position of point B1? How do you calculate that

In the isosceles triangle ABC, the angle c = 90 ° and BC = 3cm, if the center point O of AC is taken as the rotation center Rotate the triangle 180 ° and point B falls at B1. How many centimeters has point B changed from the original position of point B1? How do you calculate that

This problem is nothing more than the distance from point B to point B1
First of all, according to the known conditions, this triangle is an isosceles right triangle
Point O is the midpoint of the right angle side of AC, Bo = (the square of 3 + the square of 1.5)
=(3 / 2) times the root 5
So the length of BB1 is 2BO = 3 times the root 5

In △ ABC, ab = AC, rotate △ ABC around point B to get △ a'bc '
If the degree of rotation is exactly equal to half of the base angle, and C 'is on AC, it is proved that △ a' MB is an isosceles triangle

It is estimated that M is the intersection of a'c 'and AC, which is proved by this assumption
It is proved that: in ∵ ⊿ ABC, ab = AC, C 'is over AC, ∠ ABC' = ∠ C 'BC
∴BC=BC’ ∠C=∠BC’C=∠ACC’+∠A,∠ACC’=∠A=36°
Then ⊿ a'mb is an isosceles triangle

As shown in the figure, D, e and F are the points on the sides BC, AC and ab of △ ABC, DF ⊥ De, and △ CDE can coincide with △ BDG after rotating 180 ° clockwise around point D, so as to verify BG + BF > EF

1) It is proved that in △ BFD and △ CED, BD = CD, be = CE, ∠ DFB = ∠ Dec = 90 degrees
Then: △ BFD and △ CED are congruent
Then ∠ B = ∠ C
So delta ABC is an isosceles triangle

As shown in the figure, in △ ABC, ab = 12, AC = BC = 10, points D and E are on edge AB and AC respectively, and ∠ CDE = ∠ a, let BD = x, CE = y. find the functional relationship between Y and X

∵AC=BC，∴∠A=∠B，∵∠BDE=∠CDE+∠BDC=∠A+∠AED，∠CDE=∠A，∴∠AED=∠BDC，∴△ADE∽△BCD，∴AEBD＝ADBC，∴10−yx＝12−x10，∴y＝110x2−65x+10．