Question

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

Answer 1

Part 1)
`51\ units`

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

`RS=NP`

`ST=PQ`

`RT=NQ`

In this problem we have

`RT=7x-5` ----> equation A

`NQ=5x+11` ----> equation B

so

equate equation A and equation B

`7x-5=5x+11`

`7x-5x=11+5`

`2x=16`

`x=8\ units`

Find the length of side RT

`RT=7x-5` ----->
`RT=7(8)-5=51\ units`

therefore

`RT=NQ=51\ units`

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