You found the relationship between the angle measures of a triangle. Recognize and apply properties of inequalities to the measures of the angles.

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Presentation transcript:

You found the relationship between the angle measures of a triangle. Recognize and apply properties of inequalities to the measures of the angles of a triangle. Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle. Then/Now

Concept

List the angles of ΔABC in order from smallest to largest. Order Triangle Angle Measures List the angles of ΔABC in order from smallest to largest. Answer: C, A, B Example 2

List the angles of ΔTVX in order from smallest to largest. A. X, T, V B. X, V, T C. V, T, X D. T, V, X Example 2

List the sides of ΔABC in order from shortest to longest. Order Triangle Side Lengths List the sides of ΔABC in order from shortest to longest. Answer: AC, AB, BC Example 3

List the sides of ΔRST in order from shortest to longest. A. RS, RT, ST B. RT, RS, ST C. ST, RS, RT D. RS, ST, RT Example 3

Concept

Identify Possible Triangles Given Side Lengths A. Is it possible to form a triangle with side lengths of 6 , 6 , and 14 ? If not, explain why not. __ 1 2 Check each inequality.  X Answer: Example 1

Identify Possible Triangles Given Side Lengths B. Is it possible to form a triangle with side lengths of 6.8, 7.2, 5.1? If not, explain why not. Check each inequality. 6.8 + 7.2 > 5.1 7.2 + 5.1 > 6.8 6.8 + 5.1 > 7.2 14 > 5.1 12.3 > 6.8  11.9 > 7.2  Since the sum of all pairs of side lengths are greater than the third side length, sides with lengths 6.8, 7.2, and 5.1 will form a triangle. Answer: yes Example 1

B. Is it possible to form a triangle given the side lengths 4. 8, 12 B. Is it possible to form a triangle given the side lengths 4.8, 12.2, and 15.1? A. yes B. no Example 1

In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR? A 7 B 9 Find Possible Side Lengths In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR? A 7 B 9 C 11 D 13 Example 2

In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ? Example 2