1.)given triangle rst is congruent to triangle npq, rt=7x-5, nq=5x+11, fine the length of side rt and side nq
a.)8
b.)51
c.)40
d.)56
2.)which of the following statements is true about the triangles below?
a.) triangle abc is congruent to triangle def by ssa
b.) triangle abc is congruent to triangle def by aas
c.) triangle abc is congruent to triangle def by aas
d.) triangle abc is congruent to triangle def by asa

Part 1)

Part 2) The triangle ABC and triangle DEF are congruent by SAS

Step-by-step explanation:  

Part 1)

we know that

If the triangle RST is congruent to triangle NPQ

then

their corresponding sides are congruent

In this problem we have

----> equation A

----> equation B

so

equate equation A and equation B

Find the length of side RT

----->

therefore

Part 2)

we know that  

The SAS states that triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles

therefore

The triangle ABC and triangle DEF are congruent by SAS

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

25/6 hope it : )

step-by-step explanation: