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

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

4. Answer Acute, equiangular, equilateral, isosceles Back

5. Classifying Triangles for $200 Define: Isosceles Triangle

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

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

8. Answer Isosceles, Right Back

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

10. Answer Scalene Back

11. 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 E C F D B

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

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

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

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

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

17. 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

18. Answer m<B = m<Q => 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

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

20. Answer Back

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

22. Answer Yes, ASA or AAS Back

23. 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.

24. Answer Yes, Hypotenuse – Leg Congruence Back

25. 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

26. Answer Hypotenuse – Angle Congruence Back

27. 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

28. Answer Leg- Leg Congruence Back

29. 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.

30. Answer Yes, Hypotenuse – Leg Congruence Back

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

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

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

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

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

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

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

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

39. 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 B C A D

40. Answer Back

41. 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 B C A D

42. Answer Back

43. 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

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

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

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

47. 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

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

49. 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.

50. Answer 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 C (b,c) S (b/2,c/2) T ((a+b)/2,c/2) B (a,0) A (0,0) Back