MATH 305 Topics for Test 1, Spring 2014

Note: This includes some exercises that were not assigned but that relate to the topic listed.

TOPICS

RELATED PROBLEMS

Chapter 1

  • using The Geometer’s Sketchpad
  • constructing geometric objects
  • basic language of geometry
  • inscribed angles and central angles in a circle, and how they are related
  • cyclic quadrilaterals

 

  •  
  • A1, A2, A3, A6, A7, A8
  • E4, E7, E15, E16, E21, E28
  • A4,A5

  • A9, E20

Chapter 2

  • negations and implications
  • congruent triangles
  • exterior angle of a triangle and its relation to the other angles
  • transversals on parallel lines
  • constructions

 

  • A5, A6, A7, E12, E13
  • A1, E4, E5
  • A8, E16, E25
  • A9, A10
  • A2, A3, A4, E30b

Chapter 3

  • more on negations and implications
  • Pythagorean Theorem
  • altitudes, medians, angle bisectors, perpendicular bisectors of sides
  • points defined by concurrence: orthocenter, etc.
  • proving congruence of triangles
  • circumcircle of a triangle
  • Ceva’s Theorem and its converse

 

  • A1. A2, E11, E15
  • A3, E6, E9
  • A4, A5, A6, A7, E29a

  • A4, A5, A6, A7, E42
  • E16, E19, E20, E21
  • E31, E43
  • A9, A10, E37, E38, E39

Chapter 4

  • cyclic quadrilaterals
  • calculating the power of a point (three methods)
  • why the three methods for power are equivalent
  • arbelos
  • incircles and excircles of a triangle
  • radical axis

 

  • A1, A2, E8, E14
  • A3, A5, A6, E3
  • E27
  • A7, E29a
  • A8, E15
  • E18, E19, E21