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Presentation transcript:

Warm-Up

Triangle Inequalities Objectives – Students will investigate the inequalities among sides and angles in triangles. Students will also discover the exterior angle conjecture through the use of class notes and activities.

Draw a Triangle You might need two or three tries until you can draw this triangle correctly. Do your best to triangle a triangle where one side is 2 inches, one side is 3 inches, and the last side is 4 inches.

Draw a Triangle You might need two or three tries until you can draw this triangle correctly. Do your best to draw a triangle where one side is 2 inches, one side is 2 inches, and the last side is 5 inches.

Draw a Triangle You might need two or three tries until you can draw this triangle correctly. Do your best to draw a triangle where one side is 2 inches, one side is 3 inches, and the last side is 5 inches.

Take a Guess! What do you think the Triangle Inequality Conjecture is?

Scalene Triangle Draw a scalene triangle as best as you can Measure the lengths of each side of the triangle Label the biggest side “b”, label the side in the middle “m”, and label the smallest side “s”. Now, measure all three angles in your triangle. Label the biggest angle “B”, the middle angle “M”, and the smallest angle “S”. Do you notice any pattern?

Take a Guess! What do you think the Side-Angle Inequality Conjecture is?

Let’s Practice! Order the angles from greatest to least B 3 inches

What about if the sides are equal? What do we know about angles A and B? 3 inches 3 inches A B

Exterior Angles If we extended one of the sides of a triangle, we create an exterior angle Angle “x” is the exterior angle here

Exterior Angles What relationship is there between angle “x” and the angles “a” and “c”?

Why does this work?