Q:

I don’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, ....

Accepted Solution

A:
Answer: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)