Sure, let's analyze the problem step by step, given the side lengths of a triangle [tex]\(a, b,\)[/tex] and [tex]\(c\)[/tex] and determine which statement is not true.
Let's consider the sides of the triangle given as:
- [tex]\( a = 5 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = 7 \)[/tex]
We need to verify the following statements about the triangle:
1. [tex]\( a - b > c \)[/tex]
2. [tex]\( a + b > c \)[/tex]
3. [tex]\( a - b < c \)[/tex]
4. [tex]\( a + c > b \)[/tex]
Now let's go through each statement one by one and check their validity:
1. [tex]\( a - b > c \)[/tex]
- Substitute values: [tex]\( 5 - 3 > 7 \)[/tex]
- Simplification: [tex]\( 2 > 7 \)[/tex]
- This is not true.
2. [tex]\( a + b > c \)[/tex]
- Substitute values: [tex]\( 5 + 3 > 7 \)[/tex]
- Simplification: [tex]\( 8 > 7 \)[/tex]
- This is true.
3. [tex]\( a - b < c \)[/tex]
- Substitute values: [tex]\( 5 - 3 < 7 \)[/tex]
- Simplification: [tex]\( 2 < 7 \)[/tex]
- This is true.
4. [tex]\( a + c > b \)[/tex]
- Substitute values: [tex]\( 5 + 7 > 3 \)[/tex]
- Simplification: [tex]\( 12 > 3 \)[/tex]
- This is true.
By analyzing each statement:
- [tex]\( a - b > c \)[/tex] results in [tex]\( 2 > 7 \)[/tex], which is false.
- The rest of the statements are true.
Therefore, the statement that is not true for the given triangle is:
[tex]\[ \boxed{a - b > c} \][/tex]
