6.4 Triangle Inequalities. Angle and Side Inequalities  Sketch a good size triangle in your notebook (about a third of the page).  Using a ruler find.

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Presentation transcript:

6.4 Triangle Inequalities

Angle and Side Inequalities  Sketch a good size triangle in your notebook (about a third of the page).  Using a ruler find the approximate length of each side (in inches or centimeters).  How is the largest side related to the largest angle?  How is the smallest angle related to the smallest side?

Name the angles in ascending order.

Name the longest side. 43 Name the shortest side. o o o

TRIANGLE INEQUALITY THEOREM  The sum of the lengths of any two sides of a triangle is greater than the length of the third side.  Is it possible for a triangle to have the following lengths? 3, 6, 8 10, 10, = 9 > = 11 > = 14 > 3YES = 10.5 > = 20 > 0.5 YES

Get on your “ Thinking Caps ”  Can you think of three lengths that cannot make a triangle?

More Triangle Inequality Practice  The lengths of two sides of a triangle are 3 and 5. The length of the third side must be greater than and less than

Put the following angles in ascending order.

Section 6.4 #17

PRACTICE MAKES PERFECT!  Page 221  #1 – 16

Extra Credit Opportunity (SAT style!)  What is the smallest integer, x, for which x, x + 5, and 2x – 15 can be the lengths of the sides of a triangle?  Hint: Use the Triangle Inequality Theorem