Chapter 2 Test 8 Key

NAME KEY DATE SCORE Test 8 Chapter 2 Test Directions: Write answers in the spaces provided. 1. Use the conditional: If I and 2.2 are right angles, then angle 1 equiv angle2 a. Write the hypothesis. 12 ARE PT. 25 b. Write the conclusion. 12 c. Write the converse, IFI 22, THEN LICZ ARE RT. S d. Is the converse true or false? 2. Justify each statement with a property from algebra. Answers 1. a. (See question) (3) b. (See question) (3) C (See question) (3) FALSE (3) 2. (See question) (8) Statements Reasons 3. LEGF LUGI (2) 1. 4x + 3 = - 5(x + 3) 1. Given equation 2. 4x + 3 = - 5x - 15 2. DISTRIBUTIVE PROP. 1. LEGI & LIGJ (2) 3. 4x + 18 = - 5x 3. ADDITION PROP. LEGF CFGJ (2) 4. 18 - 9x 4. SUBTRACTION PROP. 4. MIDPH. TH. (3) 5. - 2 = x 5. DivisioN PROP. 5. Def. OF (3) 3. In the diagram, overline GJ overleftrightarrow EI Name: 6. REFLEXIVE (3) 7.BISECTOR TH (3) a. two acute vertical angles b. two congruent supplementary angles E G 8. DEF OF COMP 443) e. two adjacent complementary angles H 2. ADJACENT (3) Name the definition, property or theorem that justifies each statement. 10. (4) 4. If D is the midpoint of overline AC , then AD = 1/2 * AC 5. If angle ABC is a right angle, then AB 1 BC. 6. overline BC equiv overline BC 7. If vec BD ; the bisector of ABC, then n angle CBD = 1 2 angle ABC. B 2 A 11. (3) 58 deg 12. (3) (52 deg)/0 D angles. 9. If two lines are perpendicular, then they form congruent 7 = 20+ 8. m angle1+m angle 2 = 90 , then angle 1 and angle 2 are complementary angles. Complete each statement. 10. If a supplement of an angle is 20 more than three times a - complement, then the measure of the angle is ? (VERTICAL ARE) 13. (3) 70 deg C 14. (3) 32 deg Questions 4-8 10) 80 - x = 3(90 - x) + 20 55 110 8 70 P 11. m angle TPU = eta/n W 12. (..) m angle YPS = underline ? R 13. (") m angle. WPX = underline ? 14. A complement of YPX has measure? (90-58) Questions 11-14 (continued) 3(x) 2x = 110 NAME KEY DATE SCORE Test 8 (continued) 15. Given: vec MC perp overleftrightarrow AE and vec MB perp vec MD a. Find the value of x. b. Find the measure of BMC. +23 B (5x+10) M E 16. Rewrite the following biconditional as two conditionals that are converses of each other. Two lines are perpendicular if and only if they meet to form right angles. IF 2 LINES ARE perp THEN THEY FORM RT. C5. IF 2 LINES FORM RT.ES, THEN THEY ARE 17. Complete the proof by supplying the missing statements and reasons. Given: 22 are comp. 4; W Prove: angle XYZ = angle ABC Proof: 2 Y A Answers 15. a. 13 (3) b. 75 deg (3) 16. (See question) (4) 17. (See proof) (15) 18. (See proof) (15) #15) 5x+10+x+2+90=180 X 78 13 = 90-13-2=75 M angle BMC = 90 - x - 2 6x C Statements 1. angle 1 and angle 2 are comp. 4. 3. m angle XYZ =m angle1+m angle2 4. m angle XYZ = 90 5. AB 1 BC 6. m angle ABC = 90 7. m angle. XYZ =m angle ABC, or angle XYZ = angle ABC 18. Write a two-column proof. Reasons 1. Given 2. Def. of complementary angles 3. PasTULATE 4. SUBSTITUTION 5. Given 6. DEF. OF 7. SUBSTITUTION/TRANSITIVE STATEMENTS PEASONS Given: angle 3 and angle 4 are supp. 4. Prove: angle 1 equiv angle2 1.) 43 ELA ARE SUPPLs GiveN 2 2.) 23+24=180 DEF. of supp. 25 3.) angle 1 + 24 = 180 < POSTULATE 4) angle 3 + 24 =21+ angle4 SUBSTITUTION 5.) 44 24 REFLEXIVE 6.) 43 ان SUBTRACTION 7.22 43 VERTICAL LE ARE SUBSTITUTION 8.) 42521 angle 1 + L * 2 = 90 deg overline AB perp overline BC