Me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me

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.  

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.

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,

, so =5 ;

, so  

Now, draw the image of RST i.e R'S'T'

Since, [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

In the triangle ABD and triangle CBD, we have

  (SIDE)            [Given]

  (SIDE)            [Reflexive post]

Since, there is no included angle in these triangles.

∴ 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)            [Reflexive post]

therefore by, SSS postulates .

3)

Given that:   are vertical angles, as they are formed by intersecting lines.

Therefore

, by the definition of linear pairs

and and  and are linear pair.

By linear pair theorem, and   are supplementary, and  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, .