Question

Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).

∆ABC and ∆FDE are congruent by the ____criterion. (Use the three-letter abbreviation without spaces.)
The value of x is_____ and the value of y is_____
.

Answer 1

Not sure about the first part but X is 11 because if 14 is congruent to x + 3 then you just do 14-3 which is 11 and then since you figured out x is 11 you just plug that into 11-y and so if it needs to equal 3 then 11-3 = 8. So basically x=11 y=8

Answer 2

∆ABC and ∆FDE are congruent by the SSS criterion

The value of x is 11 and the value of y is 8.

Explanation:

By the given diagram,

AB = FD ⇒ AB ≅ FD,

BC = ED ⇒ BC ≅ ED,

CA = EF ⇒ CA ≅ EF,

By SSS ( side-side-side ) congruence postulate,

Δ ABC ≅ Δ FDE

Now, BC = ED ⇒ x + 3 = 14 ⇒ x = 11

Also, AB = FD ⇒ 3 = x - y ⇒ 3 = 11 - y ⇒ 3 - 11 = - y ⇒ -8 = -y ⇒ y = 8