Question

∆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:

ΔABC and ΔFDE are congruent by the postulate SSS

Equate the congruent sides in the 2 triangles

BC = ED, that is

x + 3 = 14 ( subtract 3 from both sides )

x = 11

-------------------------------------

DF = AB, that is

x - y = 3 ← substitute x = 11

11 - y = 3 ( subtract 11 from both sides )

- y = 3 - 11 = - 8 ( multiply both sides by - 1 )

y = 8

Answer 2

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

Explanation:

It is given that ∆ABC and ∆FDE are congruent.

The corresponding parts of congruent triangle are congruent.

`AB=FD` (CPCTC)

`3=x-y` .... (1)

`BC=DE` (CPCTC)

`x+3=14`

Subtract 3 from both the sides.

`x=14-3`

`x=11`

The value of x is 11.

Put x=11 in equation (1).

`3=11-y`

Add y on both the sides.

`3+y=11`

Subtract 3 from both the sides.

`y=11-3`

`y=8`

The value of y is 8.