Math 3 Review Sheet Ch. 3 November 17-18, 2011 Before you begin studying for a test, it is impotent to take stock of what you know and what you need to review. Below I have listed the topics covered during this unit as well as important topics covered in chapter 2. Directions: Number each part with a 1, 2 or 3. • a 1 stands for a topic you still have trouble with or find confusing. These are your first priority. • a 2 stands for a topic you know, but you may be confused about the details. These are your second priority. • a 3 stands for a topic you feel you know well. You could explain this topic to someone else. These are your third priority. 1. Topics (a) Congruent Complements and Supplements (Ch. 2) (b) Addition and Subtraction Properties (Ch. 2) (c) Multiplication and Division Properties (Ch. 2) (d) Transitive and Substitution properties (Ch. 2) (e) Vertical Angles (Ch. 2) (f) Proving Triangles Congruent (Ch.3 - 3.2) i. ASA ii. SAS iii. SSS iv. AAS v. HL-Postulate (g) CPTCTC (h) Circles (i) Altitudes (j) Medians (k) Overlapping Triangles i. Reflexive Property: Angles , Sides (l) Definitions and Types of Triangles i. Scalene ii. Isosceles iii. Equilateral iv. Right v. Acute vi. Obtuse (m) Longest side is across from the largest angle, etc. (n) Angle ⇒ Sides and Sides ⇒ Angles Now that you have prioritized the topics you need to focus on, you can more effectively choose the problems to work on. I have collected a large selection of problems, they range in difficulty. You should look through the problems and find those relevant to your priorities. You do not need to complete all the problems, however, you should work on a selection from each level of difficulty (easy, medium, hard). Do not start with the hardest ones!!! Easy: 2, 10, 11, 13, 14, 18 Medium: 3, 4, 5, 6, 12, 15, 19 Hard: 7, 9, 16, 17 Very Challenging: 8 Tests are made up of mostly medium problems with some easy problems and some hard problems. 2. What additional information is needed to prove these triangles congruent? What postulate would you then use to prove triangles congruent? Try to come up with more than one way to solve this problem. E F A B C D 3. Prove the following: (You may not use the Isosceles Triangle Theorem or its converse) Given: ∠1 ∼ = ∠2 A BC ∼ = BC 1 Prove: 4ABC is Isosceles. B 2 C 4. Prove the following: Given: 4ADC is isosceles A B is the midpoint of AD B D Prove: 4ABC ∼ = 4DBC C 5. Prove the following: Given: ∠L is trisected. L 4F LA is isosceles. Prove: 4LM F ∼ = 4LOA M F A O 6. Prove the following: Given: T is the midpoint of M S P Q ∠P M T and ∠QN T are right ∠1 ∼ = ∠2 MR ∼ = SN Prove: ∠P ∼ = ∠Q S R 2 1 M T N 7. Prove: Given: CB ∼ = CD A B ∠ABD ∼ = ∠EDB D C CB and CD trisect ∠ACE. Prove: 4ABE ∼ = 4EDC E 8. Prove (this one is challenging) Given: AD ∼ = DB A B AE ∼ = BC F H G CD ∼ = ED C E Prove: 4AF B is isosceles. D 9. Prove: Given: AD ∼ = CF E B ∠BAC ∼ = ∠DF E G ∠ABC ∼ = ∠DEF A Prove: 4DGC isosceles D C F 10. Prove: −−→ Given: F H bisects ∠GF J and ∠GHJ. G 2 3 1 4 H F Prove: F G ∼ = FJ J 11. Prove: Given: ∠5 ∼ = ∠6 ∠JHG ∼ = ∠O ∼ GH = M O Prove: ∠J ∼ = ∠P J P 5 G 6 H M O 12. Prove: Given: ∠N ∠S ∠N P O N S ∠SP R ∠N P O ∼ = ∠SP R N∼ = SP Prove: 4N OP ∼ = 4SRP P O R 13. Given: ∠1 ∠2 ∠3 ∠4 Prove: ∠1 ∼ = ∠4 4 2 1 3 14. P Given: P K and JM bisect each other at R. M R Prove: P J ∼ = MK J K 15. Prove: (Do not use the definition of isosceles or the isosceles triangle theorem) F Given: JG is an altitude and a median FJ ∼ = HJ. G Prove: 4F JG ∼ = 4HJG H J 16. J Given: JK ∼ = MK −→ OP bisects JK and M K O Prove: JO ∼ = PK M P K 17. Prove: Given: HO ∼ = MO H M JO ∼ = KO O HJ is an altitude of 4HJK M K is an altitude of 4M KJ Prove: ∠M KJ ∼ = ∠HJK J K 18. A Given: ∠ADB ∼ = ∠ADC 4ABC is isosceles Prove: AD is a median B D C 19. Prove: Given: KG ∼ = GJ ∠2 ∼ = ∠4 G F H ∠1 is comp to ∠2 ∠3 is comp to ∠4 ∠F GJ ∼ = ∠HGK Prove: F G ∼ = HG 3 1 2 K 4 J

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