Idon’t understand this. triangles abc and pqr are given. triangle abc is congruent to pqr by sas. if angle abc=12x+2, angle pqr= 142-2x,

The true statements:

- AB = 8

- x is seven units greater than y

- m∠ABC = 122°

Step-by-step explanation:

* One case of congruence is SAS that means

- If two sides and including angle between them in the first

 triangle equal to the corresponding sides and angle in the

 second triangle, then the two triangles are congruent

* In the problem

- Triangle ABC is congruent to triangle PQR using SAS case

* That means

- AB = PQ

- BC = QR

- m∠ABC = m∠PQR  

- Where angle ABC including angle between AB and BC

  and angle PQR is the including angle between PQ and QR

* Now we will use the information about the lengths of AB

 and PQ to find y, and use the measures of angles ABC and

 PQR to find x and then chose the correct answer

∵ m∠ABC = 12x + 2

∵ m∠PQR = 142 - 2x

∵ m∠ABC = m∠PQR

∴ 12x + 2 = 142 - 2x ⇒ collect the like terms

∴ 12x + 2x = 142 - 2

∴ 14 x = 140 ⇒ divide both sides by 14

∴ x = 10

* Lets substitute this value of x to find the m∠ABC and m∠PQR

- m∠ABC = 12(10) + 2 = 120 + 2 = 122°

- m∠PQR = 142 - 2(10) = 142 - 20 = 122°

∵ AB = 5y - 7

∵ PQ = 3y - 1

∵ AB = PQ

∴ 5y - 7 = 3y - 1 ⇒ collect the like terms

∴ 5y - 3y = -1 + 7

∴ 2y = 6 ⇒ divide both sides by 2

∴ y = 3

* Lets substitute this value of y to find the AB and PQ

- AB = 5(3) - 7 = 8 units

- PQ = 3(3) - 1 = 8 units

* Lets check the answer to chose the right answer

- 1st answer ⇒ AB = 8 (√)

- 2nd answer ⇒ m∠PQR = 140° (x)

- 3rd answer ⇒ y = 1 (x)

- 4th answer ⇒ x is seven units greater than y (√)

  ( x = 10 and y = 3 then x - y = 10 - 3 = 7)

- 5th answer ⇒ m∠ABC = 122° (√)

- 6th answer ⇒ PQ = 3 (x)

step-by-step explanation:

answers available in this download

(pearson%2c%25202012)%2520bbs.pdf& usg=aovvaw1obmtxnfghfgxhx0urh_je

24/56=hx^7

step-by-step explanation: