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Geometry: Unit 4 Congruent Triangles

Geometry: Unit 4 Congruent Triangles

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Geometry: Unit 4 Congruent Triangles

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  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.