Name Class Date Practice 5-7 Form K Inequalities in Two Triangles Write an inequality relating the given side lengths. If there is not enough information to reach a conclusion, write no conclusion. 1. AB and CB AB R CB A To start, determine whether the triangles have two pairs of congruent sides. B D 100 AD > CD C DB > 9 DB Then compare the hinge angles. u 80 m/ z ADB z 5 u m/CDB 5 100 2. JL and MO JL S MO 3. ST and BT no conclusion N K 60 S B 44 J M T 30 35 C O L 4. Two identical laptops are shown at the right. Top edge In which laptop is the distance from the top edge of the screen to the front edge of the keyboard greater? Explain. 45 Laptop B; the lengths of the laptops’ keyboards and screens are the same. Laptop B is open wider, so the hinge angle is greater than it is for Laptop A. A Front edge Algebra Find the range of possible values for each variable. 5. (3x 15) D 6. 48 66 (2x 4) 28 C 23 F u x , 27 50 25 E m/CDF , m/EDF m/CDE . 0 x. 16 2 ,x, u u 5 u Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 65 70 B Name Class Date Practice (continued) 5-7 Form K Inequalities in Two Triangles Use the diagram at the right for Exercises 7–9. Complete each comparison with R or S. Then complete the explanation. A D C 46 90 u 7. m/ACB S m/DCE 45 B 45 z lDCE z forms a straight angle with z lBCE z and z lACB z. u The measure of /DCE is 44 . u 8. AB S DE u u Because nBCE is an isosceles triangle, BC 5 CE . z kACB z and z kDCE z have two pairs of congruent sides. u So, by the 9 Theorem, AB S DE. u Hinge 9. BE S CE The longest side of a n is opposite the angle with the 9 measure. greatest 10. The diagram shows two paths that lead through a park. Would a jogger run a greater distance on Path A or Path B? Explain. Path A; the paths have two pairs of congruent sides, but Path A angles off at 268, while Path B angles off at 258. The longer side is the one opposite the greater angle. i B Path 25 26 Pat hA 12. m/U and m/X mlU R mlX 11. m/M and m/R mlM S mlR M N U 4 V O 7 P 10.5 9 4 8 2m i Write an inequality relating the given angle measures. 4 2m 11 W X Q 9 4 Y R 10.5 12 Z MN , MO, PR, and QR are 9. congruent u NO S PQ Prentice Hall Foundations Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 66 E

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