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G Triangle Inequality Theorem
供稿人: Cason

 The triangle inequality theorem states that the length

of a side of a triangle is always less than the sum of

the lengths of the other two sides.

The smallest side plus the medium side of a triangle

must be larger than the largest side.  Otherwise, it could

not close to  make a triangle. 

S + M > L

 

If we subtract the medium one from both sides,

that means the small side must be larger than the large

side minus the medium side.

S + M > L

   - M         - M

S        > L - M

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get the range for the missing side.

The two known sides for a triangle are 5 inches and 8

inches.  If the largest side is missing, it must be smaller

than 5 + 8 or 13 inches.  If the smallest side is missing,

it must be larger than 8 - 5 or 3 inches. 

 

Therefore, the missing side must range between

3 inches and         inches.  It must be larger than

3 inches and smaller than 13 inches or it will not

form a triangle.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get the range for the missing side.

The two known sides for a triangle are 3 inches and 7

inches.  If the largest side is missing, it must be smaller

than 3 + 7 or 10 inches.  If the smallest side is missing,

it must be larger than 7 - 3 or 4 inches. 

 

Therefore, the missing side must range between

4 inches and         inches.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

The two known sides for a triangle are 3 inches and 2

inches.  If the largest side is missing, it must be smaller

than 3 + 2 inches.  If the smallest side is missing,

it must be larger than 3 - 2 inches. 

 

Therefore, the missing side must range between

       inches and         inches.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

The two known sides for a triangle are 7 inches and 10

inches.  If the largest side is missing, it must be smaller

than 7 + 10 inches.  If the smallest side is missing,

it must be larger than 10 - 7 inches. 

 

Therefore, the missing side must range between

       inches and         inches.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

The two known sides for a triangle are 6 inches and 8

inches.  If the largest side is missing, it must be smaller

than 6 + 8 inches.  If the smallest side is missing,

it must be larger than 8 - 6 nches. 

 

Therefore, the missing side must range between

       inches and         inches.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

 

The two known sides for a triangle are 3" and 8"

 

Therefore, the missing side must range between

       inches and         inches.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

 

The two known sides for a triangle are 4" and 7".

 

Therefore, the missing side must range between

       inches and         inches.

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

 

The two known sides for a triangle are 7" and 10".  What

is the range for the missing side?

    " <  x  <      "

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

 

The two known sides for a triangle are 14" and 17".  Solve

for the missing side.

    " <  x  <      "

Since S + M > L and S > L - M, if we know two sides of a

triangle, we can get a range for the missing side.

 

The two known sides for a triangle are 12" and 16".

What are possible values for the missing side?

    " <  x  <      "

The two known sides for a triangle are 12" and 20".

What are possible values for the missing side?

    " <  x  <      "

The two known sides for a triangle are 12" and 6".

What are possible values for the missing side?

    " <  x  <      "

The two known sides for a triangle are 14" and 20".

What are possible values for the missing side?

    " <  x  <      "

The two known sides for a triangle are 14" and 30".

What are possible values for the missing side?

    " <  x  <      "

The two known sides for a triangle are 14" and 16".

What are possible values for the missing side?

    " <  x  <      "
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