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Name _______________________________________ Date __________________ Class __________________ Practice A Angle Relationships in Triangles Use the figure for Exercises 1–3. Name all the angles that fit the definition of each vocabulary word. 1. exterior angle __________________ 2. remote interior angles to 6 __________________ 3. interior angle __________________ For Exercises 4–7, fill in the blanks to complete each theorem or corollary. 4. The measure of each angle of an _______________ triangle is 608. 5. The sum of the angle measures of a triangle is _______________. 6. The acute angles of a _______________ triangle are complementary. 7. The measure of an _______________ of a triangle is equal to the sum of the measures of its remote interior angles. Find the measure of each angle. 8. mB ___________________ 9. mF __________________ 10. mG ___________________ 11. mL ___________________ 12. mP ___________________ 13. mVWY _______________ 14. When a person’s joint is injured, the person often goes through rehabilitation under the supervision of a doctor or physical therapist to make sure the joint heals well. Rehabilitation involves stretching and exercises. The figure shows a leg bending at the knee during a rehabilitation session. Use what you know about triangles to find the angle measure that the knee is bent from the horizontal (fully extended) position. ________________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ Practice C 11. 7; 7; 4 1. 228 ft 8 in. 2. 83 ft 2 in. Challenge 3. For ABC, x 1 or 1 because the triangles are isosceles, x2 1, so x 1. For DEF, x 1 because a length cannot be negative, and if x 1 then EF 1. So x 1 is the only solution for DEF. 4. ABC must be isosceles and DEF must be an equilateral triangle. 5. GH GI 25, HI 9; GH GI 9, HI 1 6. Possible answer: By the Corr. Angles Postulate, mA = m21 = m23 60° and mG m14 m24 60. Construct a line parallel to CE through D. Then also by the Corr. Angles Postulate, mD m22 m1 m15 m12 60. By the definition of a straight angle and the Angle Add. Postulate, m1 + m4 + m21 180, but m1 m21 mA 60. Therefore by substitution and the Subt. Prop. of Equality, m4 60. Similar reasoning will prove that m11 m18 m19 60. By the Alt. Int. Angles Theorem, m19 m20 and m18 m16. m20 m10 and m16 m5 by the Vertical Angles Theorem. By the Alt. Int. Angles Theorem, m4 m2 and m5 m7 and m10 m8 and m11 m13. By the definition of a straight angle, the Angle Addition Postulate, substitution, and the Subt. Prop., m17 m6 m3 m9. Substitution will show that the measure of every angle is 60 . Because every angle has the same measure, all of the angles are congruent by the definition of congruent angles. 1. 16 3. 3 5. 27 2. 7 4. 1 6. 21 57 7. 8. 12 9. 21 10. 36 11. Answers will vary. Problem Solving 1. 3 frames 2. 4 3 3 1 ft; 4 ft; 5 ft 8 8 4 3. Santa Fe and El Paso, 427 km; El Paso and Phoenix, 561 km; Phoenix and Santa Fe, 609 km 4. scalene 5. B 6. J Reading Strategies 1. scalene, obtuse 2. equilateral, equiangular, acute 3. isosceles, right 4. isosceles triangle 5. no such triangle 6. scalene right triangle ANGLE RELATIONSHIPS IN TRIANGLES Reteach 1. 3. 5. 7. 9. right acute acute isosceles isosceles 2. 4. 6. 8. 10. obtuse right obtuse scalene 9; 9; 9 Practice A 1. 1, 4, 6 2. 2, 3 3. 2, 3, 5 4. equiangular 5. 180 6. right 7. exterior angle 8. 115° Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date __________________ Class __________________ 9. 70° 10. 60° 11. 65° 12. 35 13. 120° 14. 110° Practice B 2. 45° 3. 45.1° 5. 89.7° 4. z° 6. 60° 7. 47° 8. 33°; 66°; 81° 11. 55° 47° 2. 38° 14 mR 85°; mS 30°; mT 65° 49° 6. 39.8° 7. (90 x)° 9. 41° 11. 33°; 33° 1. 101.1° 9. 44°; 44° 1. 3. 4. 5. 8. 51° 10. 82°; 82° Challenge 10. 108°; 108° 1. 39° 12. 54°; 72°; 54° 3. Through C, draw line || BA . So is also || DE. Then apply the Alt. Int. Thm. twice, followed by the Add. Post. x° 55° 62° 117°. Practice C 2. 88° 1. Possible answer: Statements Reasons 1. Quadrilateral ABCD 1. Given 2. Draw AC. 2. Construction 3. mD mDAC mDCA 3. Triangle Sum Thm. 180°, mB mBAC mBCA 180° 4. Additional Answer: Proofs will vary. Given: ABC with exterior angle BCD Prove: mBCD m1 m2 Proof: 4. mD mDAC mDCA 4. Add. Prop. of mB mBAC mBCA 360° 5. mDAC mBAC mDAB, mDCA mBCA mDCB 5. Angle Add. Post. 6. mD mDAB mB mDCB 360° 6. Subst. Statements 2. 3. 360 4. interior 540°; exterior 360° 5. x 93; y 52; z 35 Reteach Reasons 1. ABC with exterior angle BCD 1. Given 2. Through C, draw line parallel to AB . 2. Through a point outside a line, there is exactly one line parallel to the given line. 3. m1 m3 3. lines corr. s 4. m2 m4 4. lines alt. int. s 5. mBCD m3 m4 5. Add. Post. 6. mBCD m1 m2 6. Subst. Prop. of Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry