TOPIC 1 FOUNDATIONS OF GEOMETRY 1 1 MEASURING

TOPIC 1: FOUNDATIONS OF GEOMETRY

1 -1 MEASURING SEGMENTS AND ANGLES HOMEWORK: 15 -35

IN THIS CHAPTER I CAN… • 1 -1: Use correct notation and add segments and angles • 1 -2: Use a compass to draw basic constructions • 1 -3: Calculate distances and midpoints • 1 -4: Use inductive reasoning identify patterns, make predictions, and create counterexamples • 1 -5: Write if-then conditional statements • 1 -6: Use deductive reasoning to draw conclusions from conditional statements • 1 -7: Write a proof

VOCAB Point Has a location but no size A Line Has infinite points in a straight path that extends without end in opposite directions B Segment A part of a line that has endpoints CD Ray A part of a line with one endpoint and extends without end in one direction Opposite Two rays with a common endpoint and Rays extends without end in opposite directions Angle Plane Two rays with a common endpoint that is also a vertex Has infinite points and lines on a flat surface and extends without end in all directions E A B C D E GF and GH F G H J KJ and KL M K L M

EXAMPLES B A If AB = 3 x+1, BC = 2 x+2, and CB =16, find AC. AB = 3(7)+1 = 22 BC = 2(7)+2 = 16 AC = 38 C

EXAMPLE B 8 A 11 D C G F E GE = GF + FE GE = 11 + 8 GE = 19

EXAMPLE A If ABC = 86 and BD is an angle bisector, find ABD. D 43 B C