Cho tam giác ABC vuông tại A , đường cao AH. Gọi D là điểm đối xứng với H qua AB , gọi E là điểm đối xứng với H qua AC . a) Chứng minh rằng D đối xứng với E qua A
b) Tam giác DHE là tam giác gì ? Vì sao
c) Chứng minh BC = BD + CE

-
English version :

Let ABC be a right triangle at A, altitude AH. Let D be the point of symmetry with H through AB , let E be the point of symmetry with H through AC .
a) Prove that D is symmetric about E through A
b) What is the triangle DHE? Why
c) Prove BC = BD + CE

i will take them

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

b. ol

step-by-step explanation:

i got the answer right on edg.

congruent: (geometry) (of figures) identical in form; coinciding exactly when superimposed.