Question

Triangle E F G is shown. Which statements regarding Triangle E F G are true? Select three options. E F + F G greater-than E G E G + F G greater-than E F E G minus F G less-than E F E F minus F G greater-than E G E G + E F less-than F G

Answer 1

Answer:

options 1 ( E F + F G greater-than E G ), 2 (E G + F G greater-than E F ) and 5 ( E G + E F less-than F G ) are true.

Step-by-step explanation:

Given triangle EFG.

In each tirangle with sides lengths a, b and c, we always have

$a+b>c\\ \\a+c>b\\ \\b+c>a$

In triangle EFG:

• $EF+FG>EG;$
• $EG+GF>EF;$
• $FE+EG>FG.$

So, options 1 ( E F + F G greater-than E G ), 2 (E G + F G greater-than E F ) and 5 ( E G + E F less-than F G ) are true.

Options 3 and 4 are false.

Answer 2

The statements regarding triangle E F G are true ,Options 1 ( E F + F G greater-than E G ) and  option 2) (E G + F G greater-than E F ) and option 5 ( E G + E F less-than F G ).

In each triangle with sides lengths a, b and c, we always have

Given triangle EFG we have,

What is the relation between sides of the triangle?

The addition of two side is grater than the third side of triangle.

$a+b > c$

$a+c > b$

$b+a > c$

So by the above relation we get,In triangle EFG,

$EF+FG > EG\\EG+GF > EF\\FE+EG > FG$

So by the above assumption we can conclude that,

The options 1 ( E F + F G greater-than E G ), 2 (E G + F G greater-than E F) and 5 ( E G + E F less-than F G ) are true. and options 3 and 4 are false.

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