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

Below

Explanation:

got it right

Answer 2

*See attachment for the given diagram.

Answer:

∆ABC and ∆FDE are congruent by the SSS criterion.

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

Explanation:

Based on the Side-Side-Side (SSS) Congruence Theorem, ∆ABC and ∆FDE are congruent to each other. The 3 sides of ∆ABC are congruent to the 3 given sides of ∆FDE.

Thus:

AB ≅ DF

BC ≅ DE

CA ≅ FE

Find x:

Since BC ≅ DE, therefore measure of BC = measure of DE.

BC = x + 3

DE = 14

Thus,

x + 3 = 14

Subtract 3 from each side

x = 14 - 3

x = 11

Find y:

Since AB ≅ DF, therefore the measure of both sides are equal.

AB = 3

DF = x - y

Thus,

x - y = 3

Substitute x = 11 into the equation

11 - y = 3

Subtract 11 from both sides

-y = 3 - 11

-y = -8

Divide both sides by -1

y = -8/-1

y = 8