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Presentation transcript:

Follow the directions and complete both sides of the activity Get the explore activity, a ruler and a protractor for each person and one bag of straws for every 4-5 students Follow the directions and complete both sides of the activity

5.5 Inequalities in one triangle What is an inequality? What is this picture trying to tell me??

List the sides of the triangle in order from shortest to longest: List the angles in order from largest to smallest: ST, RS, RT <L, <K, <J

Triangle Inequality Theorem The sum of any two sides of a triangle must be greater than the length of the third side.

4 < x < 20 12, 8, ? Add: 12 + 8 = 20 Subtract: 12-8 = 4 12, 8, ? Add: 12 + 8 = 20 The missing side must be between these numbers. Subtract: 12-8 = 4 4 < x < 20

Describe the possible lengths of the third side of the triangle. Is it possible to construct a triangle with the given side lengths? Explain. A) 6, 7, 11 B) 3, 6, 9 Describe the possible lengths of the third side of the triangle. C) 5 inches, 12 inches ________ D) 2 meters, 4 meters ________ 6 + 7 > 11 ?? YES 3 + 6 > 9 NO 7 < x < 17 2 < x < 6

Imagine you need to prop open the mouth of an alligator…

Who would need the longer stick?

5.6 inequalities in two triangles What can I figure out about <BAC and <DAC??

Hinge Theorem If two sides in one triangle are congruent to two sides in another triangle, AND the included angle of the first is larger than the included angle of the second, THEN the third side of the first in longer than the third side of the second. The converse is also true! Since 53º is greater than 47º (and there are two congruent, corresponding sides) then QL is longer than LW.

MJ is longer since it is across from the larger angle. Which Put in fake numbers for the angles… 20° 50° MJ is longer since it is across from the larger angle.

How does <PST compare to <SPR if ST and PR are congruent? Write and solve an inequality to describe the restriction on the value of x: <PST > <SPR since it is across from the longer side. 4x – 3 > 2x 2x > 3 2x + 5 < 66 2x < 61 x < 30.5 x > 1.5

Complete with <, >, or =: