3. $100 $200 $300 $400 $500 $200 $300 $400 $500 Classifying Triangles Proving Congruence Coordinate Proof Congruence in Right Triangles Isosceles Triangles

4. Classifying Triangles for $100 Classify the following triangle by sides and angles. Give all possible names:

5. Answer Acute, equiangular, equilateral, isosceles Back

6. Classifying Triangles for $200 Define: Isosceles Triangle

7. Answer Isosceles Triangle – A three sided polygon where two or more sides are congruent Back

8. Classifying Triangles for $300 Classify the following triangle by sides and angles. Give all possible names:

9. Answer Isosceles, Right Back

10. Classifying Triangles for $400 Classify the following triangle by sides and angles. Give all possible names:

11. Answer Back Scalene

12. Classifying Triangles for $500 Given that the two triangles below are congruent, then triangle ABC is congruent to _____. Also, identify the congruent, corresponding parts. A B C D E F

13. Triangle ABC is congruent to Triangle EDF. AB = ED BC = DF AC = EF <A = <E <B = <D <C = <F Answer Back

14. Proving Congruence for $100 List all the ways to prove congruence in right triangles:

15. Answer HA – Hypotenuse- Angle HL – Hypotenuse - Leg LL – Leg - Leg LA – Leg - Angle Back

16. Proving Congruence for $200 List all the ways to prove congruence in triangles:

17. Answer ASA – Angle – Side – Angle SAS – Side – Angle – Side AAS – Angle – Angle – Side SSS – Side – Side - Side Back

18. Proving Congruence for $300 Given triangle ABC is congruent to triangle PQR, m<B = 3x+4, and m<Q = 8x-6, find m<B and m<Q

19. Answer m CPCTC 3x+4 = 8x – 6 10 = 5x 2 = x m<B = 3x+ 4 = 3*2+4 = 10 degrees m<Q = 8x-6 = 8*2-6 = 10 degrees Back

20. Proving Congruence for $400 Given: RS = UT; RT = US Prove: Triangle RST = Triangle UTS

21. Answer Back StatementsReasons RS = UTGiven RT = USGiven ST = STReflexive Property of Congruence Triangle RST is congruent to triangle UTS SSS

22. Proving Congruence for $500 Can you prove that triangle FDG is congruent to triangle FDE from the given information? If so, how?

23. Answer Back Yes, ASA or AAS

24. Congruence in Right Triangles for $100 Is it possible to prove that two of the triangles in the figure below are congruent? If so, name the right angle congruence theorem that allows you to do so.

25. Answer Back Yes, Hypotenuse – Leg Congruence

26. Congruence in Right Triangles for $200 Given that AD is perpendicular to BC, name the right angle congruence theorem that allows you to IMMEDIATELY conclude that triangle ABD is congruent to triangle ACD

27. Answer Back Hypotenuse – Angle Congruence

28. Congruence in Right Triangles for $300 Name the right angle congruence theorem that allows you to conclude that triangle ABD is congruent to triangle CBD

29. Answer Leg- Leg Congruence Back

30. Congruence in Right Triangles for $400 Is there enough information to prove that triangles ABC and ADC are congruent? If so, name the right angle congruence theorem that allows you to do so.

31. Answer Yes, Hypotenuse – Leg Congruence Back

32. Congruence in Right Triangles for $500 What additional information will allow you to prove the triangles congruent by the HL Theorem?

33. Answer AC is congruent to DC or BC is congruent to EC Back

34. Isosceles Triangles for $100 If a triangle is isosceles, then the ___________ are congruent

35. Answer Back If a triangle is isosceles, then the base angles are congruent

36. Isosceles Triangles for $200 The angle formed by the congruent sides of an isosceles triangle is called the ____________

37. Answer Back The angle formed by the congruent sides of an isosceles triangle is called the vertex angle

38. Isosceles Triangles for $300 Name the congruent angles in the triangle below. Justify your answer: A B C

39. Answer Back <A <C by the Isosceles Triangle Theorem

40. Isosceles Triangles for $400 Given ABC is an equilateral triangle, BD is the angle bisector of <ABC, Prove that triangle ABD is a right triangle A B C D

41. Answer Back StatementsReasons AB = BC = AC BD is the angle bisector of <ABC Given <ABD = <DBCDefinition of Angle bisector <ABD = 60 degreesDefinition of a equilateral triangle <ABD+<DBC = 60Angle Sum Theorem <ABD + <ABD = 60Substitution <ABD = 30Simplify <BAD = 60Definition of a equilateral triangle <BAD + <ADB + <ABD = 180 degreesTriangle Sum Theorem 60 + 30 + <ADB = 180Substitution ADB = 90Simplify Triangle ABD is a right triangleDefinition of right triangles

42. Isosceles Triangles for $500 Given ABC is an isosceles right triangle, and BD is the angle bisector of <ABC, Prove that triangle ABD is isosceles A B C D

43. Answer Back StatementsReasons AB = BC ABC is a right triangle BD is the angle bisector of <ABC Given <ABD = <DBCDefinition of Angle bisector <ABD = 90 degreesDefinition of a right, isosceles triangle <ABD+<DBC = 90Angle Sum Theorem <ABD + <ABD = 90Substitution <ABD = 45Simplify <BAC = <BCDIsosceles Triangle Theorem <BAC + <BCA + <ABC = 180 degreesTriangle Sum Theorem <BAC + <BAC + 90 = 180Substitution <BAC = 45Simplify <BAC = <ABDSubstitution AD = BDIsosceles Triangle Theorem Triangle ABD is isoscelesDefinition of Isosceles Triangles

44. Coordinate Proof for $100 Draw the following triangle on a coordinate plane. Label the coordinates of the vertices: An equilateral triangle where the length of the base is 2a and the height is b

45. Answer Back A (0,0) B (2a,0) C (a,b)

46. Coordinate Proof for $200 Draw the following triangle on a coordinate plane. Label the coordinates of the vertices: A Scalene Triangle

47. Answer Back A (0,0) B (a,0) C (b,c)

48. Coordinate Proof for $300 Draw the following triangle on a coordinate plane. Label the coordinates of the vertices: An isosceles triangle with base a and height c

49. Answer Back A (0,0) B (a,0) C (a/2,c)

50. Coordinate Proof for $400 Write a coordinate proof to prove that if a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side.

51. Answer Back A (0,0) B (a,0) C (b,c) S (b/2,c/2)T ((a+b)/2,c/2) ST = √(((a+b)/2) – (b/2))^2 + (c/2 – c/2)^2) ST = √((a/2)^2 + 0) ST = a/2 AB = √(((a-0)/2) – (b/2))^2 + (0 -0)^2) AB = √((a)^2 + 0) AB = a Thus, ST = ½ AB

52. Coordinate Proof for $500 Use coordinate proof to prove that a triangle with base a and height b such that the vertex aligns vertically with the midpoint of the base is isosceles

53. Answer Back A (0,0) B (a,0) C (a/2,b) CA = √((a/2 – 0)^2 + (b – 0)^2) CA = √((a/2)^2 + b^2) AB = √((a – a/2)^2 + (b -0)^2) AB = √((a/2)^2 + b^2) Thus CA = AB so Triangle ABC is Isosceles