Question

Which statements about the diagram are true? Select three
options.
DE + EF > DF
A DEF is an isosceles triangle.
5 O
A DEF is a scalene triangle.

Answer 1

Answer : The correct options are:

DE + EF > DF

5 < DF < 13

Δ DEF is a scalene triangle.

Step-by-step explanation :

As we know that there are three types of triangle.

(1) Equilateral triangle : It is a triangle in which the three sides and angle are equal.

(2) Isosceles triangle : It is a triangle in which the two sides and two angle are equal.

(3) Scalene triangle : It is a triangle in which the three sides and angle are not equal.

Now we have to determine the length DF.

using Pythagoras theorem:

$(Hypotenus)^2=(Perpendicular)^2+(Base)^2$

$(9)^2=(Perpendicular)^2+(4)^2$

$81=(Perpendicular)^2+16$

$(Perpendicular)^2=81-16$

$(Perpendicular)^2=65$

$Perpendicular=8.06$

The length DF = 8.06 unit

So, we can say that:

DE + EF > DF

Hence, from the given options we conclude that, the correct options are:

DE + EF > DF

5 < DF < 13

Δ DEF is a scalene triangle.

Answer 2

The three options that are correct are;

1. DE + EF > DF  
2. 5 < DF < 13
3. A DEF is a scalene triangle.

Looking at the diagram again, we can see that it has symbol of an unequal triangle on the 3 sides. This proves number 3 correct.

• A scalene triangle is a triangle with 3 unequal sides or angles

Again, if you look at the number on the sides, we see that DE is 4 and EF is 9. If we add DE and EF together, we get that they both are longer than DF. Thus,

• DE + EF > DF

And lastly, we know that DF is less than both DE and EF. We also know that both DE and EF are equal to 13. This means that DF < 13. If DF is less than 13, we also know that the side is greater that 5. Essentially,

• 5 < DF < 13

Learn more about scalene triangles here https://brainly.com/question/12261793