Question

HELPPPPP

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

Answer 1

answer is the first one and the last 2

Answer 2

1, 3 and 4 are true statements.

Explanation:

Notice that the given triangle has all three side different, that means it's an scalene triangle.

Additionally, the triangular inequality states that the sum of two sides of a triangle must be greater than the third side, that is

`DE+EF>DF\\DE+DF>EF\\DF+EF>DE`

So, the first choice is also correct.

Then, we use thes triangular inequalities to find the third true statement.

We know that
`DE=4` and
`EF=9`

`DE+EF>DF\\4+9>DF\\DF<13`

Also,

`DE+DF>EF\\4+DF>9\\DF>9-4\\DF>5`

Therefore,
`5<DF<13`, which means side DF must be between 5 and 13.

The third true statement is the third option.