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). Two congruent triangles B A C and D E F. Side A B equals 3 equals side D F equals x minus y. Side B C equals x plus 3 equals side D E equals 14. ∆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

(X= 11) (Y= 8)

Explanation:

In the given problem, we have two congruent triangles, ΔABC and ΔFDE. Let's solve for the values of x and y:

1. From the information given, we know that side AB is congruent to side DF, and side BC is congruent to side DE.

2. It is given that AB = 3 and DF = x - y. Since the two sides are congruent, we can set up an equation: 3 = x - y.

3. Similarly, BC = x + 3 and DE = 14. Again, since the two sides are congruent, we can set up another equation: x + 3 = 14.

4. Solve the second equation for x: x = 14 - 3 = 11.

5. Substitute the value of x into the first equation: 3 = 11 - y.

6. Solve the equation for y: y = 11 - 3 = 8.

Therefore, the value of x is 11, and the value of y is 8.