Question

Find all possible solutions for x such that △ABC is congruent to △DEF. One or more of the problems may have no solution.

16. △ABC: sides of length 6, 8, and x. △DEF: sides of length 6, 9, and x - 1.

17. △ABC: sides of length 3, x + 1, and 14. △DEF: sides of length 13, x - 9, and 2x - 6

18. △ABC: sides of length 17, 17, and 2x + 1. △DEF: sides of length 17, 17, and 3x - 9

19. △ABC: sides of length 19, 25, and 5x-2 △DEF: sides of length 25, 28, and 4 - y

Answer 1

one abbreviation used below triangle = tr

Explanation:

16] as tr ABC is congruent to tr DEF

which means that AB= DE BC=EF AC=DF

acc to given 6 in there in both

8 is there and 9 in other so in which 9 is not there the unknown value there has to be 9 which means x = 9

in triangle, DEF 8 is not there so x-1=8 ---->x=9

17] Similarly in this one 3 and 14 are sides of tr ABC and tr DEF only side is known which is 13 so the unknown side in tr ABC has to be 13

x+1=13 -----> x = 12

in tr, DEF 2 sides are unknown which has to be 3 and 14

so 2 cases will become either x-9= 3 or x-9=14

x-9=3 x-9=14

x=12 x=23

18] In this the given known values of sides of both the tr's is same

so it will become

2x+1=3x-9

9+1 = 3x-2x

-----> x=10

19] in this one only 1 of the known values is same so in tr ABC the unknown has to 28 and the unknown in tr DEF has to be 19

5x-2 = 28 4-y=19

5x= 30 y= 4-19

x=6 y = -15

I hope this helps

I am not confirm whether my answer is correct or not but i tried my best

thanks