1. 7-4: Triangle Inequality Theorem

2. Theorem 7-9 (Triangle Inequality Theorem): The sum of the measures of any two sides of a triangle is greater than the measure of the third side. We use the Triangle Inequality Theorem to determine if three sides can form a triangle.

3. 7-4: Triangle Inequality Theorem Determine if the three numbers can be measures of the sides of a triangle.  5, 7, 4  5 + 7 > 4true  5 + 4 > 7true  7 + 4 > 5true  Since all cases are true, these measures can form a triangle.  11, 3, 7  11 + 3 > 7true  11 + 7 > 3true  3 + 7 > 11false  Since there is at least one false statement, these measures cannot form a triangle.

4. 7-4: Triangle Inequality Theorem Y OUR T URN DDetermine if 16, 10, and 5 can be the measures of the sides of a triangle. If not, explain. NNo, 5 + 10 is not greater than 16

5. If you are given two sides to a triangle, then the unknown side must be:  Less than the sum of the known sides, and  Greater than the difference of the known sides Example  If two sides of a triangle are 17 and 8, find the range of possible measures for the third side.  17 + 8 = 25  17 – 8 = 9  The third side must be 9 < x < 25

6. 7-4: Triangle Inequality Theorem Y OUR T URN IIf two sides of a triangle are 9 and 13, find the range of possible measures for the third side. 44 < x < 22

7. Assignment  Worksheet #7-4 Tomorrow  Quiz on 7-1 through 7-3 Monday  Distribution of chapter 7 preview Wednesday  Chapter 7 test