10. Let the measure of the third side be n . 57 1 32 ¬ . n 57 1 n ¬ . 32 32 1 n ¬ . 57 89 ¬ . n or n , 89 n ¬ .2 25 n ¬ . 25 Graph the inequalities on the same number line. n ¬ , 89 n ¬ .2 25 n ¬ . 25 Find the intersection. The range of values that fit all three inequalities is 25 , n , 89. Inequalities Involving Two Triangles Pages 270–271 Check for Understanding 1. Sample answer: A pair of scissors illustrates the SSS inequality. As the distance between the tips of the scissors decreases, the angle between the blades decreases, allowing the blades to cut. 2. The SSS Inequality Theorem compares the angle between two sides of a triangle for which the two sides are congruent and the third side is different. The SSS Postulate states that two triangles that have three sides congruent are congruent. 3. In n BDC and n BDA , B w C w > A w D w , B w D w > B w D w , and m / BDA . m / CBD . The SAS Inequality Theorem allows us to conclude that AB , CD . 4.
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