Question

Which statement is true about figure DEF?​

Answer 1

Side DF is congruent (the = and ~ symbol) to side DE

Answer 2

The correct option is A)
`\overline{DF}\cong \overline{DE}`

Explanation:

Consider the provided figure.

The coordinates of E is (-2,3)

The coordinates of D is (-5,1)

The coordinates of F is (-3,-2)

Now use the distance formula to find the length of line segment:

`\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad √(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

The distance between (-2,3) and (-5,1) is:

`\overline{DE}=√(\left(-5-\left(-2\right)\right)^2+\left(1-3\right)^2)=√(13)`

The distance between (-5,1) and (-3,-2) is:

`\overline{DF}=√(\left(-3-\left(-5\right)\right)^2+\left(-2-1\right)^2)=√(13)`

The distance between (-3,-2) and (-2,3) is:

`\overline{EF}=√(\left(-2-\left(-3\right)\right)^2+\left(3-\left(-2\right)\right)^2)=√(26)`

Hence the length of line segment DE and DF is same.

Thus the correct option is A)
`\overline{DF}\cong \overline{DE}`