Please help me this is due and im so confused??? extra points

HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME HELP ME

Kryger [21]

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 $\frac{5}{3}$ 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 $\frac{5}{3}$

Since, the center of dilation at S(2,-2) is not at the origin, so the point S and its image $S{}'$ 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 $\frac{5}{3}$ of each of these distances,

$SR=3$ , so $S{}'R{}'$ =5 ;

$ST=3$ , so $S{}'T{}'=5$

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

Since, $RT=3\sqrt{2}$ [By using hypotenuse of right angle triangle] and $R{}'T{}'=5\sqrt{2}$ .

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 $\overline{AC}$ i.e $\overline{AB}\cong \overline{BC}$

In the triangle ABD and triangle CBD, we have

$\overline{AB}\cong \overline{BC}$ (SIDE) [Given]

$\overline{BD}\cong \overline{BD}$ (SIDE) [Reflexive post]

Since, there is no included angle in these triangles.

∴ $\Delta ABD$ is not congruent to $\Delta CBD$ .

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 $\overline{AD}\cong \overline{CD}$ .