Answer:
1)
Given the triangle RST with Coordinates  R(2,1), S(2, -2) and T(-1 , -2).
A dilation is a transformation which produces an image that is the same shape as original one, but is different size.  
Since, the scale factor  is greater than 1, the image is enlargement or a stretch.
 is greater than 1, the image is enlargement or a stretch.  
Now, draw the dilation image of the triangle RST with center (2,-2) and scale factor 
Since, the center of dilation at S(2,-2) is not at the origin, so the point S and its image  are same.
 are same.
Now, the distances from the center of the dilation at point S to the other points R and T.  
The dilation image will be of each of these distances,
 of each of these distances,
 , so
, so  =5 ;
=5 ;
 , so
, so  
  
Now, draw the image of RST i.e R'S'T'
Since,  [By using hypotenuse of right angle triangle] and
 [By using hypotenuse of right angle triangle] and  .
.
2)
(a) 
Disagree with the given statement.
Side Angle Side postulate (SAS) states that:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then these two triangles are congruent.
Given: B is the midpoint of  i.e
 i.e 
In the triangle ABD and triangle CBD, we have 
 (SIDE)            [Given]
   (SIDE)            [Given]
 (SIDE)            [Reflexive post]
   (SIDE)            [Reflexive post]
Since, there is no included angle in these triangles.
∴  is not congruent to
 is not congruent to  .
 .
Therefore, these triangles does not follow the SAS congruence postulates.
(b)
SSS(SIDE-SIDE-SIDE) states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. 
Since it is also given that   .
.
therefore, in the triangle ABD and triangle CBD, we have 
 (SIDE)            [Given]
   (SIDE)            [Given]
 (SIDE)           [Given]
   (SIDE)           [Given]
 (SIDE)            [Reflexive post]
   (SIDE)            [Reflexive post]
therefore by, SSS postulates  .
. 
3)
Given that:   are vertical angles, as they are formed by intersecting lines.
 are vertical angles, as they are formed by intersecting lines. 
Therefore
, by the definition of linear pairs 
 and
 and  and
 and  and
  and  are linear pair.
 are linear pair.
By linear pair theorem,  and
 and  are supplementary,
   are supplementary,  and
 and  are supplementary.
  are supplementary.


Equate the above expressions:

Subtract the angle 2 from both sides in the above expressions
∴
By Congruent Supplement theorem: If two angles are supplements of the same angle, then the two angles are congruent.
therefore,  .
.