Question

If triangle ABC = DEF AB = 8 , BC = 19 , AC = 14 , EF = 4x - 1 and DE=y-6, what are the values of x,y, and z

Answer 1

x = 5 and y = 14

Explanation:

Given
`\triangle`ABC
`\cong \triangle`DEF.

Congruent triangles have congruent corresponding parts, so

`AB\cong DE\\ \\AC\cong DF\\ \\BC\cong EF`

Since

`AB=8\\ \\BC=19\\ \\AC=14\\ \\EF=4x-1\\ \\DE=y-6,`

then

`4x-1=19\\ \\4x=19+1\\ \\4x=20\\ \\x=5`

and

`y-6=8\\ \\y=8+6\\ \\y=14`