Geometry: Unit 4 Congruent Triangles

1. Geometry: Unit 4 Congruent Triangles VOLK SPRING 2014

2. Unit 4 Preview in Numbers • Instructional Days: 6 • Review Days: 1 • Test Days: 1 • Total Homework Problems: About 120 • New Theorems: ? • New Postulates: ? • New Definitions: ?

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 theorem to test/prove triangles congruent. • Use HL theorem 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 • Hypotenuse-Leg (HL) 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. Hypotenuse-Leg (HL) Congruence Theorem • If the hypotenuse and one adjacent side of a right triangle are congruent to the hypotenuse and an adjacent side in another triangle, then the two triangles are congruent.

29. Classwork

30. Classwork

31. Classwork

32. Homework • Homework Set 4.2 (4 pages) • DUE TOMORROW so DO TODAY!

33. Triangle Proofs II Lesson 4.3

34. 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.

35. 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.

36. New Definitions • None Today

37. New Postulates • None Today

38. New Theorems • None Today

39. Key Points of Triangle Proofs

40. Key Points of Triangle Proofs • Start with given statements and reasons • Look for givens in the diagram • Last statement is in the question. • Last reasons: SSS, SAS, ASA, AAS, or HL • Annotate the diagram • Look for reflexive sides • Look for vertical Angles • Use definitions

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