Lesson 5-5: Inequalities in Triangles

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Presentation transcript:

Lesson 5-5: Inequalities in Triangles

Angle-Side Relationship Think of two flashlights shining on a wall • The flashlight with the widest opening makes a longer segment on the opposite wall, similarly… ► The widest angle has the longest side opposite to it. ► The narrowest angle has the shortest side opposite to it.

Write the measurements of the triangles in order from least to greatest. 100˚ H J G 45˚ 35˚ 8 5 Q R P 7 SOLUTION SOLUTION JH < JG < GH m R < mQ < m P

Can you make a triangle with any 3 sides? Draw a triangle with sides 3, 6, and 8 inches Draw a triangle with sides 3, 6, and 9 inches Draw a triangle with sides 3, 6, and 10 inches.

3 Sides Inequality Any 2 sides must be greater than the 3rd side Testing 3 sides 2 smaller sides must be more than 3rd side Range for 3rd side Order sides Subtract left, add right 3rd side must be between (not equal! )

Can 13, 21, 33 be the sides of a triangle? Given 12 cm and 15 cm, what are the possibilities for the 3rd side? Two smaller sides: 13 + 21 = ? = 34 → bigger than 3rd side → YES Order, subtract left, add right 15 – 12 = 3; 12 + 15 = 27 3rd side must be between 3 and 27 → 3 < 3rd side < 27