1. Geometry: Unit 4 Congruent Triangles VOLK SPRING 2014

2. Unit 4 Preview in Numbers • Instructional Days: 8 • Review Days: 1 • Test Days: 1 • Total Homework Problems: About 120 • New Theorems: 8 • New Postulates: 5 • New Definitions: 12

3. Unit 4 Preview of Topics • Identify/Classify Triangles • SSS, SAS, ASA, AAS • CPCTC • Equilateral and Isosceles Triangles • Coordinate Plane Triangles • Bisectors, Medians, and Altitudes

4. Triangle Basics Lesson 4.1

5. Lesson 4.1 Objectives The student will be able to… • Identify and classify triangles by angles and sides • Apply the Triangle Sum Theorem. • Apply the Exterior Angle Theorem. • Name and Use CPCTC. • Prove triangles congruent by definition.

6. Virginia SOL Standard G.6 • The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

7. New Definitions • Acute Triangle • Obtuse Triangle • Right Triangle • Equilateral Triangle • Isosceles Triangle • Scalene Triangle • Auxiliary Line • Corollary • Exterior Angle • Remote Interior Angle • Congruent • Corresponding Parts

8. New Postulates • Reflexive Property of Triangle Congruence - ∆ABC ≅ ∆ABC • Symmetric Property of Triangle Congruence - If ∆ABC ≅ ∆EFG, then ∆EFG ≅ ∆ABC. • Transitive Property of Triangle Congruence - If ∆ABC ≅ ∆EFG and ∆EFG ≅ ∆JKL, then ∆ABC ≅ ∆JKL.

9. New Theorems • Triangle-Sum Theorem • Exterior Angle Theorem • Triangle Angle-Sum Corollaries • Third Angles Theorem

10. Classifying Triangles I • Acute Triangle: All three angles are acute. • Obtuse Triangle: One obtuse angle (other two acute) • Right Triangle: One right angle (other two acute)

11. Classifying Triangles II • Equilateral Triangle: All three sides are congruent. • Isosceles Triangle: Only two sides are congruent. • Scalene Triangle: No two sides are congruent.

12. Exterior Angle • Exterior Angle of a polygon can be drawn using an auxiliary line.

13. Triangle-Sum Theorem • The sum of the measures of the angles of a triangle is 180.

14. Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

15. Triangle Angle-Sum Corollaries • 1. The acute angles of a right triangle are complementary. • 2. There can be at most one right or obtuse angle in a triangle.

16. Third Angles Theorem • If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

17. Homework • Homework Set 4.1 • DUE TOMORROW so DO TODAY!

18. Triangle Proofs I Lesson 4.2

19. Lesson 4.2 Objectives The student will be able to… • Use SSS postulate to test/prove triangles congruent. • Use SAS postulate to test/prove triangles congruent. • Use ASA postulate to test/prove triangles congruent. • Use AAS postulate to test/prove triangles congruent.

20. Virginia SOL Standard G.6 • The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

21. New Definitions • Included Angle • Included Side

22. New Postulates • Side-Side-Side (SSS) Congruence Postulate • Side-Angle-Side (SAS) Congruence Postulate • Angle-Side-Angle (ASA) Congruence Postulate

23. New Theorems • Angle-Angle-Side (AAS) Congruence Theorem

24. Side-Side-Side (SSS) Congruence Postulate • If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

25. Side-Angle-Side (SAS) Congruence Postulate • If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

26. Angle-Side-Angle (ASA) Congruence Postulate • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

27. Angle-Angle-Side (AAS) Congruence Theorem • If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent.

28. Homework • Homework Set 4.2 • DUE TOMORROW so DO TODAY!

29. Triangle Proofs II Lesson 4.3

30. Lesson 4.3 Objectives The student will be able to… • Use SSS postulate to test/prove triangles congruent. • Use SAS postulate to test/prove triangles congruent. • Use ASA postulate to test/prove triangles congruent. • Use AAS postulate to test/prove triangles congruent.

31. Virginia SOL Standard G.6 • The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

32. New Definitions • None Today

33. New Postulates • None Today

34. New Theorems • None Today

35. New Information

36. Homework • Homework Set 4.3 • DUE TOMORROW so DO TODAY!

37. Triangle Proofs III Lesson 4.4

38. Lesson 4.4 Objectives The student will be able to… • Use SSS postulate to test/prove triangles congruent. • Use SAS postulate to test/prove triangles congruent. • Use ASA postulate to test/prove triangles congruent. • Use AAS postulate to test/prove triangles congruent.

39. Virginia SOL Standard G.6 • The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

40. New Definitions • None Today

41. New Postulates • None Today

42. New Theorems • None Today

43. New Information

44. Homework • Homework Set 4.4 • DUE TOMORROW so DO TODAY!

45. Equilateral & Isosceles Lesson 4.5

46. Lesson 4.5 Objectives The student will be able to… • Use properties of equilateral and isosceles triangles.

47. Virginia SOL Standard G.6 • The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

48. New Definitions • Vertex Angle • Base Angles • Legs of Isosceles Triangle

49. New Postulates • CPCTC - Corresponding Parts of Congruent Triangles are Congruent

50. New Theorems • Isosceles Triangle Theorem - If two sides of a triangle are congruent, then the angles opposite those sides are congruent. • Converse of Isosceles Triangle Theorem - If two angles of a triangle are congruent, then the sides opposite those angles are congruent. • Equilateral Triangle Corollaries (Corollaries of the Isosceles Triangle Theorem) - 1. A triangle is equilateral if and only if it is equiangular. 2. Each angle of an equilateral triangle measure 60.