Triangle Formative/Summative 1
  • Objective 1: Find the range of possible values
  • Objective 2: Determine the right triangle associated with LEG/LEG given
  • Objective 3: Determine the right triangle associated with LEG/HYP given
  • Objective 4: Classify given triple as:
    • acute scalene
    • right scalene
    • obtuse scalene
    • NOT a triangle
  • Objective 5: Rate your level of confidence and success on Objectives 1-4
    • This is as important to me as the mathematics goals, it helps me get better and more focused for you
      • I will require that you eventually complete this anyway, so please just answer all posed honestly and to best abilities
Facts that should be acquired and stored in memory
  • difference of two given sides = minimum boundary of possible third side.
  • sum of two given sides = maximum boundary of possible third side.
  • every pair of positive numbers has a pair of related right triangles associated with those two given numbers

  • Acute scalene 
    • 3 acute angles 
    • no equal sides
    • no complementary angles 
  • Right Scalene
    • follows all right triangle properties
    • 1 hypotenuse
    • 2 legs
    • 1 right angle 
    • 2 complementary acute angles 
    • no equal sides
  • obtuse scalene
    • 1 obtuse angle 
    • 2 acute angles 
    • no equal sides
NOT a Triangle
  • side length falls below the difference of the two smaller sides 
  • side length exceeds the sum of the two smaller sides
  • Equilateral
    • Also called regular triangle
    • Also called Equiangular triangular
    • most special triangle
    • all angles measure 60 degrees
    • all sides are equal
  • acute isosceles
    • 2 congruent acute bases angles 
    • 1 acute vertex angle 
    • 2 congruent legs 
    • third side need not be congruent
  • right isosceles
    • Half of a Square
    • 45/45/90 special right triangle
    • 1 hypotenuse
    • 2 congruent legs
    • 45 degree base angles
    • right angle for the vertex angle 
    • hypotenuse = leg times the square root of two
  • obtuse isosceles 
    • 2 congruent acute bases angles 
    • 1 obtuse vertex angle 
    • 2 congruent legs 
    • third side is larger than legs
​
LEG LEG Missing Hypotenuse Scenario

Right Triangle
​16/30/34 Triangle

  • turn on red circle after opening file
  • what did you notice?
  • match Theta 1 to A1 using slider 
  • match Theta 2 to A2 using slider
  • After adjusting Theta 1 and Theta 2, your triangle should appear to match up C1 with C2
    • zoom in to check validity of that idea
    • Go back and be at least four decimal places accurate with Theta 1 and Theta 2
  • in your group discuss this question
    • What can be stated if C1 and C2 both lie ON THE RED CIRCLE?
  • Use Triangle Inequality Theorem and/or the Pythagorean Theorem to JUSTIFY one of the following classifications
    • acute scalene
    • right scalene
    • obtuse scalene
    • NOT a triangle
16/30/46 Triangle ?
  • turn on red circle after opening file
  • what did you notice?
  • match Theta 1 to A1 using slider 
  • match Theta 2 to A2 using slider
  • After adjusting Theta 1 and Theta 2, your triangle should appear to match up C1 with C2
    • zoom in to check validity of that idea
    • Go back and be at least four decimal places accurate with Theta 1 and Theta 2
  • in your group discuss this question
    • What can be stated if C1 and C2 both lie on X AXIS and OUTSIDE Line Segment AB?
  • Use Triangle Inequality Theorem and/or the Pythagorean Theorem to JUSTIFY one of the following classifications
    • acute scalene
    • right scalene
    • obtuse scalene
    • NOT a triangle

Oblique Triangle
16/30/45 Triangle

  • turn on red circle after opening file
  • what did you notice?
  • match Theta 1 to A1 using slider 
  • match Theta 2 to A2 using slider
  • After adjusting Theta 1 and Theta 2, your triangle should appear to match up C1 with C2
    • zoom in to check validity of that idea
    • Go back and be at least four decimal places accurate with Theta 1 and Theta 2
  • in your group discuss this question, after matching Theta 1 and Theta 2 to A1 and A2
    • What can be stated if C1 and C2 both lie ON THE OUTSIDE OF RED CIRCLE?
  • Use Triangle Inequality Theorem and/or the Pythagorean Theorem to JUSTIFY one of the following classifications
    • acute scalene
    • right scalene
    • obtuse scalene
    • NOT a triangle

Oblique Triangle
16/30/37 Triangle

  • turn on red circle after opening file
  • what did you notice?
  • match Theta 1 to A1 using slider 
  • match Theta 2 to A2 using slider
  • After adjusting Theta 1 and Theta 2, your triangle should appear to match up C1 with C2
    • zoom in to check validity of that idea
    • Go back and be at least four decimal places accurate with Theta 1 and Theta 2
  • in your group discuss this question, after matching Theta 1 and Theta 2 to A1 and A2
    • What can be stated if C1 and C2 both lie ON THE INSIDE OF RED CIRCLE?
  • Use Triangle Inequality Theorem and/or the Pythagorean Theorem to JUSTIFY one of the following classifications
    • acute scalene
    • right scalene
    • obtuse scalene
    • NOT a triangle
This is a link to Desmos Tutorial
This is a link to Desmos Geometry Tutorial
This program has yet to develop a save feature, but you can copy and paste links.
This is a link to Desmos Teacher Website
This is a beta program still in development, so no tutorials yet

Desmos User Guide