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Transcript
Name____________________________________________________Period______Date__________ Geometry 22: Even MORE Practice Chapter 3 1. Match each term with its mathematical meaning. A. transversal I. two angles whose measures have a sum of 180 B. complementary angles II. Two coplanar lines that never intersect C. skew lines III. Two non-coplanar lines that never intersect D. parallel lines IV. A line that intersects two or more coplanar lines at two distinct points E. supplementary angles V. two angles whose measures have a sum of 90 2. Identify the following in the diagram at the right. a. two lines that are parallel to plane FGI suur b. two lines that are parallel to HL c. two lines that are skew to FG d. a pair of parallel planes e. the intersection of plane LMK and plane IGK 3. In the problems below, find the value of x. a. b. m1 3 x 17 2 m2 x 1 1 m1 95 7 x 1 2 m2 55 x 4. Use the given informatin to determine which lines, if any, are parallel. Justify each conclusion with a theorem or postulate. a. ∠ 6 is supplementary to ∠ 10 b. ∠ 3 ≅ ∠ 8 c. ∠5 is supplementary to ∠ 1 d. ∠ 2 ≅ ∠ 7 e. ∠ 4 ≅ ∠ 11 f. ∠ 9 ≅ ∠ 1 5. In the diagram below, find the missing angle measures. m1 _______ m2 _______ m3 _______ m4 _______ m5 _______ m6 _______ m7 _______ m8 _______ m9 _______ m10 _______ m11 _______ m12 _______ 6. Given that l m , find the value(s) of x and each angle. Be sure to check for extraneous solutions. a. b. m3 x 2 112 m8 16 x 131 m1 x 2 7 x m7 x 7 7. Find the missing angle measure in the images below. Note: Drawings are NOT to scale. a. b. 8. In a triangle, 1 is an exterior angle and 2 and 3 are its remote interior angles. Find the measures of 2 and 3, given that m1 = 150, m2 = 2x + 3, and m3 = 5x + 7. Sketch the image if necessary. 9. Find m1. a. b. c. 10. Find the value of each variable. a. b. c. 8. Complete the following fill-in proofs. a. Given: m n Prove: m1 m7 180 1. 2. 3. 4. 5. 6. 7. 8. STATEMENTS m n 1 and 5 are Corresponding Angles 1 5 m1 m5 5 and 7 are a linear pair REASONS 1. 2. 3. 4. 5. 6. Linear Pair Postulate 7. 8. m5 m7 180 b. Given: AB CD ; 3 1 Prove: EF GH STATEMENTS 1. 2. 3. 4. 5. 6. REASONS 4 and 2 are alternate interior angles 4 2 3 1 m3 m1 mEFG m3 m4 7. mHGF m1 m2 8. mEFG m1 m2 9. mEFG mHGF 10. 11. EFG and HGF are alternate interior angles 12. 1. Given 2. 3. 4. Definition of congruence 5. 6. 7. 8. 9. 10. Definition of congruence 11. 12. c. Given: AB CD Prove: 1 and 2 are complementary angles STATEMENTS 1. 2. 3 is a right angle 3. 4. m1 m2 m3 180 5. m1 m2 90 180 6. 7. REASONS 1. Given 2. 3. Definition of right angle 4. 5. 6. Subtraction Property of Equality 7.