Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Group action wikipedia , lookup
Multilateration wikipedia , lookup
Analytic geometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Area of a circle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Euclidean geometry wikipedia , lookup
Construction WS #3 Name______________________Per.____ Geometry A On a separate sheet of typing paper, perform the following constructions and then compare the triangles you’ve created with your partners by holding them up to the light and see if they are congruent triangles. Show all construction marks!!! 1) Construct ABC with A , B and length AB A B A 2) Construct E 3) Construct O 4) Construct B EFG with the following segments: F F OLN with the following measures for angles and segments. L O N O QRS with the following measures for angles and segment. S Q E G G R R 1 Geometry A Name ________________________ Triangle Congruence Period _______ Determine whether the following triangles are congruent. If they are congruent, write the theorem or postulate vertically, justifying each part of the theorem or postulate, and complete the triangle congruence statement. NOTE: these figures are not drawn to scale! 1. BCA __________ B _____ ___________ ___________ E _____ ___________ ___________ _____ ___________ ___________ A C D F Justification: _______________ 2. MOP __________ M A _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ P O R Justification: _______________ 3. A DON __________ O _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ J N D Justification: _______________ 2 4. Y GEO __________ O _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ R T E Justification: _______________ G 5. B C ABD __________ _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ A 6. D B I Justification: _______________ BIE __________ _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ Justification: _______________ K E ABC __________ 7. _____ ___________ ___________ B D _____ ___________ ___________ _____ ___________ ___________ Justification: _______________ 3 A 8. C E G H EGH __________ _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ E Justification: _______________ M 9. PAW __________ M _____ ___________ ___________ _____ ___________ ___________ A W C _____ ___________ ___________ Justification: _______________ P 10. B C ABD __________ _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ A D Justification: _______________ 11. P N MAP __________ _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ A Justification: _______________ M T 4 MAS __________ 12. Given : AS bisects MP; 1 2 A _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ Justification: _______________ 1 2 M P 13. Given : BD bisects ABC ; BD bisects ADC B ABD __________ _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ A C Justification: _______________ D 14. Given : MN || PT ; NO TO MNO __________ P N _____ ___________ ___________ _____ ___________ ___________ O T _____ ___________ ___________ Justification: _______________ M ABE __________ 15. Given: E is the midpoint of AD ; A D ; B C B C _____ ___________ ___________ _____ ___________ ___________ _____ ___________ ___________ Justification: _______________ A E D 5 Geometry A Coordinate Proofs NAME: _________________________ PERIOD: ___________ Show all your work on a separate sheet of E-2/graph paper! Plot the graph above and information in below: Given: A (1, 8), 2) and M is the Prove: information given on the then supply the missing the two column proof B (9, 12), C (-2, -2), D (6, midpoint of 1. AB = 1. Distance Formula 2. 3. 4. 5. 6. 7. CD = M: ( ) BM = MC = BM = MC Slope of 2. Distance Formula 3. Midpoint Formula 4. Distance Formula 5. Distance Formula 6. 7. Slope Formula 8. Slope of 8. Slope Formula 9. 9. 10. 10. 6 Plot the information given on the graph above and then supply the missing information in the two column proof below: Given: S (1, 7), M (12, 7), R (-5, -6), T (6, -6) and A is the midpoint of Prove: 1. SM = 2. RT = 3. Slope of = 1. Distance Formula 2. Distance Formula 3. Slope Formula 4. Slope of = 4. Slope Formula 5. 5. 6. 6. 7. 7. 7 Plot the information given on the graph above and then supply the missing information in the two column proof below: Given: A (-3, 2), C (-9, -4), T (-2, -2), O (3, 2), G (2, -2) and D (9, -4) Prove: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. Distance Formula 2. Distance Formula 3. Transitive Property 4. Distance Formula 5. Distance Formula 6. Transitive Property 7. Distance Formula 8. Distance Formula 9. Transitive Property 10. 8 Name______________________Per._____ List the reasons for the following statements to complete each proof. 1. Given AB || CD , Prove: ABC AC || BD DCB #38 B m j A D u C Statement 1. AB || Reason CD 2. AC || BD 3. <ABC < BCD 4. <ACB <DBC 5. BC BC 6. ABC DCB 2. Given: Prove: AD BC, AB DC AD || BC A B D Statement C Reason 1. AD BC 2. AB DC 3. AC AC 4. CAD ACB 5. <DAC < BCA 6. AD || BC 9 #37 CPCTC Name 1) Per.___ a. Are the triangles congruent? b. Why? c. Is E A ? AR ER EC CA d. Why? a. Is MES OUS ? 2) SE SU E U b. Why? c. Is MS OS ? d. Why? 3) a. Are the triangles congruent? LK UE LU UK b. Why? c. Is ULE KUE d. Why? 4) FA|| TH a. Are the triangles congruent? b. Why? c. Is AI IT ? d. Why? 5) CI IN IO IE a. Is INO ICE ? b. Why? c. Is ONI ECI d. Why? 10 Give the reason for each statement in the following proof. A B 6) Given: AD BC, AB DC Prove: AD || BC D C Statement Reason 1. AD BC 2. AB DC 3. AC AC 4. CAD ACB 5. <DAC < BCA 6. AD || BC 7. Write a two-column proof for the following. Given: RY AN : RN AY Prove: RYA ANR Statements Reasons 1 1 2 2 3 3 4 4 5 5 8. Find the measure of the numbered angles ( 1-11) in order 6 2 58 1 71 4 5 9 7 8 3 11 61 10 1 2 3 4 5 6 7 8 9 10 11 11 CHAPTER 4 REVIEW NAME ___________________Per.___ Do all work on e-2 paper in homework format #39 st 1 = Write down the five ways you can prove two triangles to be congruent!!!!! Identify as true or false. IF FALSE…re-write the statement making it correct 1. If ΔMNO ΔXYZ, then MN YZ . 2. A triangle that has only 2 congruent sides is classified as an isosceles triangle. 3. If ΔMNO ΔXYZ, then / M / Y. 4. There are three shortcuts for showing that two right triangles are congruent. 5. Given ABC & DEF , if A D and C F and AC DF , the postulate ASA can be used to prove triangle congruency. (*hint: draw a picture) 6. There are five postulates/theorems to prove that non-right triangles are congruent: SSS, SAS, ASA, AAA and AAS. 7. Given that isosceles triangle ABC DEF , if <B and <E are the vertex angles and m A x and m F y , then x = y. (*hint: draw a picture) 8. Equilateral triangles are also considered isosceles triangles. 9. If two right triangles are congruent, then their hypotenuses are also congruent. 10. Two scalene triangles will never be congruent. 11. State the theorem that can be used to prove, if possible, that the triangles are congruent. a. b. c. d. J H H G J K G F e. B E E f. 12 12. Find the measure of each angle a-h. The two lines with arrows are parallel. a c 125 d g b 110 f 125 e 115 a = _____ b = _____ c = _____ d = _____ e = _____ f = _____ g = _____ h = _____ h 13. Find the value of x. x+1 a. c. b. d. 92 45 x 70 3x - 4 2x + 1 x 40 x 23 14. Classify each triangle by its sides (scalene, isosceles, or equilateral) and its angles (acute, obtuse, right, equiangular). c. b. a. 15. Complete a 2-column proof: Given: E is the midpoint of AD ; A D ; B C Prove: AB DC B A C E D 13 16. What additional congruency would you need in order to that the triangles are congruent by the indicated method. SAS_____________ ______________ AAS_____________ ______________ ASA_____________ ______________ HL _____________ ______________ 17. Construct on your paper a triangle with given sides and included angle. M A M N M 18. What is the measure of the exterior angle in the picture shown? 110o 19. Find the distance and slope between the points. OH = _______________ slope = __________ H OT = _____________ HT = ____________ O slope = __________ T slope = __________ 14 Is this a right triangle? How do you know? What type of triangle is it? 20. If BOY EAT , find the measure of the missing angles. B E A Y O 27o 63o T m < B =___________ m < Y =_____________ m < E =_____________m < A =______________ 21. Are the two triangles congruent? _________________ Why?___________________ Given: GM \ \OT G O E ME EO M T Is GE ET ?_____________Why?___________________ 15