1. Lesson: Objectives: 4.1 Classifying Triangles  To IDENTIFY parts of triangles  To CLASSIFY Triangles by their Parts

2. Geometry 4.1 Some DEFINITIONS acute triangle obtuse triangle right triangle equiangular triangle scalene triangle isosceles triangle equilateral triangle

3. Geometry 4.1 Some DEFINITIONS POLYGON –

4. Geometry 4.1 Some DEFINITIONS POLYGON – a closed figure in a Plane

5. Geometry 4.1 Some DEFINITIONS POLYGON – a closed figure in a Plane made-up of Segments that

6. Geometry 4.1 Some DEFINITIONS POLYGON – a closed figure in a Plane made-up of Segments that intersect only at their Endpoints, called VERTICES.

7. Geometry 4.1 Some DEFINITIONS POLYGON – a closed figure in a Plane made-up of Segments that intersect only at their Endpoints, called VERTICES. TRIANGLE – a three-sided Polygon consisting of Sides, Vertices, and Angles

8. Geometry 4.1

13. Equiangular

14. Geometry 4.1 EquiangularParts of a Right Triangle

15. Geometry 4.1 Classification of Triangles Angles Acute3 Acute Angles Obtuse1 Obtuse Angle Right1 Right Angle Equiangular 3  Angles

16. Geometry 4.1

22. Classification of Triangles AnglesSides Acute3 Acute AnglesScalene No 2 sides  Obtuse1 Obtuse AngleIsosceles At Least 2 sides  Right1 Right AngleEquilateral 3 sides  Equiangular 3  Angles

23. Geometry 4.1 COORDINATE GEOMETRY Find the measures of the sides of ΔRTS. Classify the triangle by sides.

24. Geometry 4.1 You should be able to: DEFINE a POLYGON DEFINE a TRIANGLE CLASSIFY a Triangle by Type of ANGLES CLASSIFY a Triangle by Type of SIDES NAME the Parts of a RIGHT Triangle

25. Lesson: Pages: Objectives: 4.2 Measuring Angles in Triangles 189 – 192  To APPLY the ANGLE SUM Theorem  To APPLY the EXTERIOR ANGLE Theorem

26. GEOMETRY 4.2 Slide 1 of 150

27. GEOMETRY 4.2

30. 180 Theorem – The SUM of the measures of the angles of a Triangle is 180.

31. GEOMETRY 4.2 180 Theorem – The SUM of the measures of the angles of a Triangle is 180. PROVE It!

32. GEOMETRY 4.2

34. THIRD ANGLE 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.

35. GEOMETRY 4.2 THIRD ANGLE 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.

36. GEOMETRY 4.2 THIRD ANGLE Theorem – If TWO Angles of one Triangle are CONGRUENT to TWO Angles of a second triangle, then the THIRD angles of the triangles ARE CONTRUENT. PROVE It.

37. GEOMETRY 4.2 Definition: EXTERIOR ANGLE An Exterior Angle is formed by one side of a triangle and the extension of another side.

38. GEOMETRY 4.2 Definition: EXTERIOR ANGLE An Exterior Angle is formed by one side of a triangle and the extension of another side. Definition: REMOTE INTERIOR ANGLES The Interior Angles of the Triangle NOT adjacent to a given Exterior Angle are Remote Interior Angles.

39. GEOMETRY 4.2 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.

40. GEOMETRY 4.2 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. PROVE It.

41. GEOMETRY 4.2

43. 60 5 2 135 13 4

44. GEOMETRY 4.2 Definition: COROLLARY A statement that can be easily proved using a theorem is called a COROLLARY. 1.The ACUTE ANGLES of a right triangle are COMPLEMENTARY. 2.There can be at most one right or obtuse angle in a triangle.

45. GEOMETRY 4.2

46. Solve for X in each Case.

47. GEOMETRY 4.2

55. You should be able to: PROVE the TOTAL DEGREES of INTERIOR ANGLES of a Triangle DETERMINE the measure of the 3 rd Angle of a Triangle Determine the EXTERIOR ANGLE from the 2 REMOTE INTERIOR Angles STATE the Corollaries (1) Acute angles of a Right Triangle (2) Number of Right/Obtuse Angles of a Triangle

56. GEOMETRY 4.2

60. Geometry 4.1