Download Practice 3A 1. What is the converse of the statement, “If a strawberry is

Practice 3A 1. What is the converse of the statement, “If a strawberry is red, then it is ripe”? 2. What is the inverse of the statement, “If you can sing, then you can go with Sarah”? 3. Which statement has a true converse? A. If a vehicle is a car, then it has four wheels. B. If you go to Asia from the United States, then you cross an ocean. C. If you own a dog, then your pet is furry. D. If you can stand up, then you can walk. E. None of these 4. Rewrite the Segment Addition Postulate as a biconditional. If B is between A and C, then AB+BC=AC. 5. The original statement and contrapositive always have the same truth value. Which of the following is the contrapositive of the statement, “If two angles are right angles, then they are congruent.”? Practice 3B 1. Which property justifies the statement? If 4AB=8CD, then AB=2CD. 2. What conclusion can you draw from the following two statements? If you have a job, then you have income. If you have an income, then you must pay taxes. 3. Which property justifies the statement? If 4x=16, then 16=4x. 4. The Transitive Property of Equality justifies which statement below? A. If y-­‐17=g, then y=g+17. B. If AM=RS, then RS=AM. C. If 5(3a-­‐4)=120, then 15a-­‐20=120. D. If ∠J≅∠R and ∠R≅∠H, then ∠J≅∠H. E. ∠M≅∠M 5. Which property justifies the statement? If m∠J=4x+5 and x=6, then m∠J=29°. Practice 3C1 1. What is the value of x if m∠1=2x+5 and m∠2=x+61? 2. What is the value of x if m∠1=2x+5 and m∠3=x+61? 3. ∠DFG and ∠JKL are complementary angles. m∠DFG=x+5, and m∠JKL=x-­‐9. Find the measure of each angle. 4. ∠1 and ∠2 are supplementary angles. m∠1=x-­‐39 and m∠2=x+61. Find the measure of each angle. 5. What are the values of x and y? Practice 3C2 1. What is the value of x if m∠1=3x+5 and m∠2=x+13? 2. What is the value of x if m∠1=3x+5 and m∠4=x+13? 3. ∠1 and ∠3 are both complementary to ∠2. If m∠1=44°, what is m∠3? 4. ∠4 and ∠6 are both supplementary to ∠5. If m∠6=44°, what is m∠5? 5. ∠7 and ∠8 form a linear pair. What is the value of x if m∠7=3x+5 and m∠8=x+13? Practice 3D 1. If l∥m and m∠1=44°, what is m∠7? The diagram is not to scale. 2. If m∠4=75°, what must be m∠8 in order for l to be parallel to m? The diagram is not to scale. 3. If ∠3 measures 50°, what is the sum of the measures of ∠6 and ∠4? The diagram is not to scale. 4. If m∠2=50° and m∠6=130°, is l∥m? The diagram is not to scale. A. No. Corresponding angles must be congruent for the lines to be parallel. B. Yes. Corresponding angles must be congruent for the lines to be parallel. C. No. Corresponding angles must be supplementary for the lines to be parallel. D. Yes. Corresponding angles must be supplementary for the lines to be parallel. 5. Which of the following will guarantee that l∥m? A. m∠2=m∠3 B. m∠2+m∠4=180 C. m∠4=m∠6 D. m∠1=m∠8 E. m∠3+m∠7=180 Practice 3E 1. What is the value of x if l∥m, m∠1=2x+44 and m∠5=5x+38? The diagram is not to scale. 2. m∠2=6x and m∠6=120. What is the value of x for l to be parallel to m? 3. If ∠8 measures 119, what is the sum of the measures of ∠1 and ∠4? 4. If c⊥b and a∥c, what is m∠2? 5. Which lines, if any, can you conclude are parallel given that m∠1+m∠2=180? Justify your conclusion with a theorem or postulate. A. j∥k, by the converse of the Same-­‐Side Interior Angles Theorem B. j∥k, by the converse of the Alternate Interior Angles Theorem C. g∥h, by the converse of the Alternate Interior Angles Theorem D. g∥h, by the converse of the Same-­‐Side Interior Angles Theorem Practice 3F1 1. Two sides of a triangle measure 13 and 15. Which length is NOT possible for the third side? A. 2 B. 8 C. 14 D. 20 E. 27 2. For ΔJKL, LJ<JK<KL. List the angles of the triangle in order from largest to smallest. 3. Which lengths can be lengths for the sides of a triangle? A. 1, 2, 5 B. 3, 2, 5 C. 5, 2, 5 D. 7, 2, 5 E. 2, 2, 5 4. In ΔABC, m∠A=28° and m∠B=70°. Which side is the longest? 5. ΔABC has AB=7, BC=24, and CA=24. Which statement is true? A. ΔABC is an equilateral triangle. B. ΔABC is an isosceles triangle. C. ∠C is the largest angle. D. ∠B is the smallest angle. E. ∠C≅∠B Practice 3F2 1. Find the value of x for which l∥m. The diagram is not to scale. 2. What is the value of x? The diagram is not to scale. 3. What is the value of x? The diagram is not to scale. 4. A triangular playground has angles whose measures are in the ratio 8:3:9. What is the measure of the smallest angle? 5. What is the value of x? The diagram is not to scale. Given: ∠SRT≅∠STR, m∠SRT=20, m∠
STU=4x Practice 3G1 1. If ΔMNO≅ΔGHI, then which of the following is NOT true? A. ΔMON≅ΔGIH B. OM=IG C. ΔHIG≅ΔNMO D. ΔIHG≅ΔONM E. ∠GHI≅∠ONM 2. If ΔMNO≅ΔGHI, m∠M=25°, and m∠O=50°, then what is m∠H? 3. For the triangles shown, ∠D≅∠T, ∠E≅∠U and EO=UX. Which of the following statements is true? A. ΔTUX≅ΔDOE by ASA B. ΔUTX≅ΔDEO by AAS C. ΔTXU≅ΔODE by ASA D. ΔTUX≅ΔDEO by AAS E. The triangles are not congruent. 4. For the triangles shown, suppose instead that TX=DO, EO=UX, and ∠O≅∠X. Which of the following statements is true? A. ΔTUX≅ΔDEO by SAS B. ΔUTX≅ΔDEO by SSA C. ΔTXU≅ΔEOD by SAS D. ΔTUX≅ΔDEO by SSA E. The triangles are not congruent. 5. Which method can be used to prove the triangles congruent? Practice 3G2 1. What additional information do you need to prove the two triangles congruent by SAS? 2. What additional information do you need to prove the two triangles congruent by ASA? 3. Suppose TM=GL, MD=SG, and m∠M=m∠G. Which of the following statements is true? A. The triangles are not congruent. B. ΔTMD≅ΔSGL C. ΔTMD≅ΔLGS D. ΔTMD≅ΔSLG 4. Suppose TD=SG, MD=SL, and m∠D=m∠S. By what method can you prove ΔDTM≅ΔSGL? 5. Suppose TD=10 cm, DM=9 cm, TM =11 cm, SL=11 cm, and SG=9 cm. What else do you need to know in order to prove that the two triangles are congruent by SSS? Practice 3H1 1. If the measure of an angle is 78 less than the measure of its complement, what is the measure of the angle? 2. ∠A and ∠B are supplementary angles and vertical angles. What is m∠B? 3. The measure of an angle is 12 less than twice the measure of its supplement. What is the measure of the angle? 4. Which statement can be combined with its converse to form a true biconditional? A. If the measure of an angle is 30, then it is an acute angle. B. If a ray is the perpendicular bisector of a segment, then the ray divides the segment into two congruent segments. C. If two lines intersect, then the two lines are not skew. D. If an angle is a straight angle, then its sides are opposite rays. E. None of these 5. The sum of the measures of a complement and a supplement of an angle is 200. What is the measure of the angle? 6. Use the Addition Property of Equality to complete the statement. If 5x-­‐12=88, then 5x=__. 7. Identify the converse of the statement: If you study in front of the TV, then you do not score well on exams. 8. An angle is five times as large as its supplement. What is the measure of the supplement? 9. What is the contrapositive of the following conditional statement? If Peg serves pudding, then it is not Laura’s birthday. 10. What conclusion can you draw from the following two statements? If a person does not get enough sleep, that person will be tired. Evan does not get enough sleep. 11. For what value of x will lines l and m be parallel if m∠3=(2x+10)° and m∠5=(5x-­‐5)°? 12. Which two angles must have the same measure to show that lines l and m are parallel? A. ∠1 and ∠5 B. ∠1 and ∠4 C. ∠3 and ∠4 D. ∠3 and ∠8 E. ∠5 and ∠8 13. Which two angles must be supplementary to show that lines l and m are parallel? A. ∠1 and ∠4 B. ∠1 and ∠3 C. ∠3 and ∠6 D. ∠3 and ∠8 E. ∠6 and ∠2 14. What is the value of x if m∠3=(2x+10)° and m∠2=(5x-­‐5)°? 15. For what value of x will lines l and m be parallel if m∠1=(2x+10)° and m∠7=(3x+5)°? Practice 3H2 1. What additional information is needed to show that the given triangles are congruent by SAS? 2. What additional information is needed to show that the given triangles are congruent by SSS? 4. In ΔWXY, m∠W=(x-­‐22)°, m∠X=(3x+19)°, m∠Y=(x-­‐17)°. What is m∠X? 5. What is the value of x? 6. What is the value of x? 3. What additional information is needed to show that the given triangles are congruent by SAS? 7. What is the value of x? 8. In ΔABC, m∠A=48° and m∠B=80°. Which side is the shortest? 9. Which of the following set of lengths will NOT form a triangle? A. 3, 4, 5 B. 7, 5, 4 C. 4, 6, 8 D. 3, 8, 10 10. What is the value of x? E. 12, 7, 5