5: geometry and measures

• what are the 4 conditions to prove 2 triangles are congruent?


  SSS(3 sides match up),

  AAS(2 angles & side match up),

  SAS(2 sides & angle between match up),

  RHS(right angle, hypotenuse & a side match up)
• what are congruent shapes?


  same size & same shape (can be reflected & rotated)
• what are similar shapes?

  same shape but different size (can be reflected & rotated)
• what are the 3 conditions to prove 2 triangles are similar?


  all angles match up,

  all 3 sides are proportional,

  2 sides are proportional with angle between matching up
• what is a tangent to a circle?


  
line that touches a point on circumference of circle that always meets radius at 90º

  
• what do 2 radii of a circle form?


  2 radii form an isosceles triangle (won't have little tick marks on sides to remind you as it is a fact to learn)

  
• what is a chord in a circle?


  
a chord is any line drawn across/through a circle, & the line that cuts it in half (perpendicular bisector) will always go through centre of circle

  
• what are the angles at the centre & circumference like from the same 2 points (2 ends of the same cord)?


  
the angle at the centre is exactly double the angle at the circumference

  
• what angle does a triangle drawn from the 2 ends of the diameter make at the circumference of a circle?



  always make 90º angle where it hits the circumference, no matter where it hits

  
• what is a segment & what are the angles like in them?


  
all triangles drawn from a chord will have the same angle where they touch the circumference, & the 2 triangles on opposite sides of chord add to 180º

  
• what is a cyclic quadrilateral?



  a 4-sided shape with every corner touching the circumference of circle, & both pairs of opposite angles add to 180º

  
• what are tangents like from the same point outside of the circle?


  
they are always equal in length, creating 2 congruent right-angled triangles

  
• what is the alternate segment theorem?


  
the angle between a tangent & a chord is always equal to the angle in the opposite segment (angle made at circumference by 2 lines drawn from ends of chord)

  
• equation for area of circle


  $πr^2$
• equation for circumference of circle


  $πd$
• equation for area of sector in circle


  (x/360) x area of full circle
• equation for length of arc sector in circle


  (x/360) x circumference of full circle