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geometry Geometric Applications are limitless…. Geometry From the Greek words Geo = earth and metro = measure The branch of mathematics first popularized in ancient Greek culture by Thales (circa 624-547 BC) dealing with spatial relationships. There are some geometric principles we remember… 3600 There are 3600 in every circle. This initial definition allows for further angles to be identified 1800 900 450 These are some more common angles Acute Angles (less than 90O) A ABC B C Obtuse Angles (greater than O) 90 A ABC B C Acute and Obtuse Angles lead us into the study of triangles… Remember: Interior angles are found inside a triangle e i Remember: Exterior angles are found outside a triangle i e i e At this stage, check out the gizmo… Supplementary Angles (SAT) Supplementary Angles must add to 180O A + B = 180O A B Complementary Angles (CAT) Complementary Angles must add to 90O A + B = 90O A B Opposite Angle Theorem (OAT) If 2 lines intersect, then the opposite angles are equal. X O O X Shape Theorems Sum of the Angles of a Triangle Theorem (SATT) The sum of the Interior Angles of a Triangle is 180O a b a + b + c = 180O c Isosceles Triangle Theorem (ITT) The base angles of an Isosceles Triangle are equal Y X X Equilateral Triangle Theorem (ETT) X= X 60O X X Exterior Interior (EI) An exterior angle equals the sum of the opposite two interior angles. D=A+B A B D Exterior Angles (EA) The exterior angles of a triangle and a quadrilateral sum to 360O A B C A + B + C = 360O Sum of the Angles Of a Quadrilateral Theorem (SAQT) The sum of the Interior Angles of a Quadrilateral is 360O a + b + c + d = 360O a d b c Exterior Angles The exterior angles of a triangle and a quadrilateral sum to 360O A + B + C + D = 360O D A C B From the green workbook Page 214 Page 217 Page 220 Page 224 HomeFun YA!!! Page 348 1-4 Page 352 1b, c, d, f, h Page 365 1a,c 2a,b