A B C 12 We know ∠B = ∠C S TU 1214 We could write a proof to show ∠T ≠∠U *We could also prove that m ∠T > m ∠U, BUT theorem 1 tells us that!

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Presentation transcript:

A B C 12 We know ∠B = ∠C S TU 1214 We could write a proof to show ∠T ≠∠U *We could also prove that m ∠T > m ∠U, BUT theorem 1 tells us that!

AB C Complete each statement by writing. a. AC _____ AB + BC b. AC _____ AB c. BC _____ AC

 If one side of a triangle is longer than a second side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

 Name the largest angle and the smallest angle of the triangle. V U W ∠U is the LARGEST angle because it is opposite the LONGEST side (WV) ∠W is the SMALLEST angle because it is opposite the SHORTEST side (VU)

 If one angle of a triangle is larger than a second angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

 Name the longest and shortest side of the triangle. A B C 90º 30º **Always find the other angle BEFORE you answer the question!! Side AB is the LONGEST side because it is opposite the LARGEST angle (∠C) Side CB is the SHORTEST side because it is opposite the SMALLEST angle (∠A)

 The sum of the lengths of any two sides of a triangle is greater than the length of the third side. L M N LM + MN > LN MN + LN > LM LN + LM > MN

 The lengths of two sides of a triangle are 3 and 5. The length of the third side must be greater than _____ but less than _____. 5 3 x Let x be the length of the third side. x + 3 > 5 x > > x 8 > x x + 5 > 3 x > -2 28