Lets draw our triangle:
Lets use the "Law of Sines" to find our side r:
![\frac{p}{\sin P}=\frac{r}{\sin R}\rightarrow\frac{9}{\frac{1}{3}}=\frac{r}{\frac{2}{3}}\rightarrow9\times\frac{3}{1}\times\frac{2}{3}=r\rightarrow r=18](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7B%5Csin%20P%7D%3D%5Cfrac%7Br%7D%7B%5Csin%20R%7D%5Crightarrow%5Cfrac%7B9%7D%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Cfrac%7Br%7D%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Crightarrow9%5Ctimes%5Cfrac%7B3%7D%7B1%7D%5Ctimes%5Cfrac%7B2%7D%7B3%7D%3Dr%5Crightarrow%20r%3D18)
So r=18
Answer:
not congruent;not congruent;congruent;congruent;not congruent;not congruent
Explanation:
In order to be congruent,the side lengths of both triangles must be equal.
The base of triangle ABC is 2 units.the base of triangle MNP is also 2 units.the hieght of triangle ABC is 3 units;but the base of triangle MNP is not 3 units,it is 4. The triangle are not congruent.
Similarly,both ABC and EFG have a base of 2 units. However,the height of ABC is 3 while the height of EFG is 4;the triangles are not congruent.
The base of ABC and STU are both 2 units,and the height of each is 3 untis the triangles are congruent.
The base of EFG is 2,as is the base of MNP ,both triangles also have a height of 4;the triangles are congruent.
The base of EFG is 2 units,as is the base of STU . however,the height of EFG is 4 while the height of STU is 3;the triangles are not congruent.
The base of STU is 2 units, as is the base of MNP .however,the height of STU is 3 while the height of MNP is 4;the triangles are not congruent.