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Exploring Triangle Inequalities: SAS and SSS Theorems

This lesson covers the essential inequalities related to triangles, focusing on the SAS (Side-Angle-Side) and SSS (Side-Side-Side) inequalities. The SAS Inequality states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle in the first triangle is larger, then the third side of the first triangle will be longer. Similarly, the SSS Inequality states that if two sides are congruent and one triangle has a longer third side, then the angle between the congruent sides is larger. Learn to apply these theorems through practical examples and problem-solving.

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Exploring Triangle Inequalities: SAS and SSS Theorems

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  1. 5.5 Inequalities Involving TWO Triangles What you’ll learn: To apply the SAS Inequality To apply the SSS Inequality

  2. Theorem 5.13 SAS Inequality/Hinge Theorem If 2 sides of a triangle are congruent to 2 sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle. If AB=DE and AC=DF and A>D, then BC>EF E B F A D C

  3. Theorem 5.14 SSS Inequality if 2 sides of a triangle are congruent to 2 sides of another triangle and the 3rd side in one triangle is longer than the 3rd side in the other, then the angle between the pair of congruent sides in the 1st triangle is greater than the corresponding angle in the 2nd triangle. If AB=DE, AC=EF, and BC<EF, then A<B E A D B C F

  4. Write an inequality relating the given pair of angles or segment measures. 1. AB _______ CD 2. mPQS ______ mRQS 15 A D 20 B 50 15 C P 8 4 Q S 4 6 R

  5. Write an inequality describe the possible values of x. 1. 3x-3<33 and 3x-3>0 3x<36 3x>3 x<12 x>1 1<x<12 2. ½x-6<52 and ½x-6>0 ½x<58 ½x>6 x<115 x>12 12<x<115 60 cm 36 cm 33 (3x-3) 60 cm 30 cm (½x -6) 30 52 30 12 28

  6. A C Given: CDAB, mACB+mBCD<mABC+mCBDAC=BDProve: AB<CD B D • CDAB, mACB+mBCD<mABC+mCBDAC=BD • BC=BC • ABC=BCD • mACB+mABC<mABC+mCBD • mACB<mCBD • AB<CD • Given • Reflexive • Alt. int. angles  • substitution • Subtraction • SAS Inequality

  7. Homeworkp. 27110-20 all, 34-40 even, skip 38

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