1. The two triangles are similar because the two pairs of angles are equal, therefore the third angles of both triangles must also be equal.
We can call this the AAA similarity criterion
2. To find QR, we must use ratios between 2 known similar sides of both triangles,
So, QR =1.02
Let, coordinate of point A' is (x,y).
Since, A' is the symmetric point A(3, 2) with respect to the line 2x + y - 12 = 0.
So, slope of line containing A and A' will be perpendicular to the line 2x + y - 12 = 0 and also their center lies in the line too.
Now, their center is given by :
Also, product of slope will be -1 .( Since, they are parallel )
x = 2y - 1
So,
Also, C satisfy given line :
Also,
Therefore, the symmetric points is .
