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Name ________________________________________ Date __________________ Class__________________ LESSON 5-6 Reading Strategies Identify Relationships Keep two ideas in mind when considering the angles and sides of a triangle. If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle. If two sides of one triangle are congruent to two sides of another triangle and the third sides are not congruent, then the larger included angle is across from the longer third side. In these triangles, m∠Q > m∠T, which means that RS > UV. In these triangles, AB > GH, which means that m∠C > m∠F. Use the relationships above to compare the following measurements. 1. 2. Compare m∠ADB and m∠DBC. Compare ZY and WZ. _________________________________________ ________________________________________ 4. 3. Compare m∠ABC and m∠EFD. Compare QR and RS. _________________________________________ ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 5-50 Holt McDougal Geometry 9. The segments can form a triangle. Challenge 1. AB ≅ AD and AC ≅ AE because radii of the same circles are congruent. Since m∠BAC > m∠DAE, then by the Hinge Thm., BC > DE. 2. 16.5 < y < 34 10. 11 11. 130; 121 12. acute Practice B 1. 3. 0.25 < z < 3 2. 2 14 61 3. 48 4. Statements Reasons 1. JK || HL , JK ≅ HL , m∠KML > m∠HML 1. Given 2. ∠JMK ≅ ∠LMH 2. Vert. ∠s Thm. 3. ∠JKH ≅ ∠LHK 3. Alt. Int. ∠s Thm. 4. UJKM ≅ ULHM 4. AAS 5. MK ≅ MH 5. CPCTC 6. ML ≅ ML 6. Reflex. Prop. of ≅ 7. KL > HL 7. Hinge Thm. Problem Solving 1. Greatest at relaxed position; least at writing position; the length of his leg and the length of his body are the same in all three triangles. So, by the Converse of the Hinge Thm., the larger included ∠ is across from the longer third side. 4. height: 25.2 in.; width: 33.6 in. 6. 2.5; no 7. 25; yes 8. 3 10; no 9. yes; acute 10. yes; obtuse 11. yes; obtuse 12. Possible answer: The triangle is obtuse, so Kitty is correct. But Kitty did not use the Pythagorean Inequalities Theorem correctly. The measure of the longest side should be substituted for c, so 169 + 64 < 256 is the inequality that shows that the triangle is obtuse. Practice C 1. Possible answer: When using the Pythagorean Inequalities Theorem, the longest side of the triangle is substituted for c, and the angle opposite that side is determined as right, acute, or obtuse. The longest side in a triangle is opposite the largest angle. So if the angle opposite the longest side is acute, then the other two angles must also be acute. 2. the second cyclist 3. The ∠ formed by the compass when drawing the first circle is smaller. So the distance between the points of the compass is greater for the second circle. 4. B 5. 51.4 in. 2. 5. G 13; − 13 3. Possible answer: Segments must have positive lengths. A negative length does not make sense. In geometry, only positive square roots are used. Reading Strategies 1. m∠ADB < m∠DBC 2. ZY > WZ 3. m∠ABC < m∠EFD 4. QR < RS 5-7 THE PYTHAGOREAN THEOREM 2. 16 3. 8.9 4. 48 in. 5. whole numbers 6. 7.2; no 7. 11.5; no 8. 12; yes 5. 6. 18 65 7. 5000 8. Practice A 1. 26 4. no; 0.128 34; 3 34 41 2 Reteach 1. x = 12 2. x = 3. x = 4. x = 40 39 29 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A56 Holt McDougal Geometry