Grade 11: analytical geometry(quadrilaterals)

Introduction

Dear students 

this lesson will be about analytical geometry in quadrilaterals. by the end of this lesson, it is expected of you to be able to prove a type of a quadrilateral eg rectangle. find missing angles, lengths, midpoints, gradients and equations of a staright line . This includes the use of  prior knowledge in knowing types of lines (intersecting, perpendicular, bisecting and parallel lines) 

Task

         INTRO OF A LESSON

  1. for a recap or lets call it a pre-test. state 4 properties of quadrilaterals. 

         stuck?... have a short study here 

 

         CLASS  ACTIVITY 

Please do the following activity click here , number 8 from a-e. Leave your answers in surd form. 

   

            POST TEST    

 

dear student please reflect on what you have find the easiest to study and  list all that you had dificulty in undesrtanding 

 

 

 

    

Process

Dear students please summarized content examples and short notes to enlighten your knowledge and get to understand this topic. 

please after reading the notes and going through the examples do the class activity or if you feel like you need more clarity there's a video below to help you 

watch this video for quick explanations and see how everything is done with quadrilaterals 

when done with the activity and proceed to the post test and make your self reflection to help know how are we are! 

Evaluation

rubric 
  1 point   2 point  3 points  4-5 points 
introduction learner doesn't show an understanding of quadrilaterals. which is also evidence that the learners didn't study    learners shows the understanding and managed to recall 1 correct  property  learner managed to this of 2 properties of quadrilaterals, which shows some understanding  learner stated all the asked properties which make it easy to proceed to the lesson development  
development (class activity)  learner shows no understanding . learners still need to go back to the prior lesson.   learner can understand some part of the work, misconception is shown   learner understand 60 % of the work. mistakes and errors here and there but concepts are understood  excellent learner, 100% understanding of the covered work 
conclusion  learner doesn't know what she knows  learner still needs guidance in unpacking concepts  learner understands where she made mistakes and why  learner needs challenging  questions

 

Conclusion

Summary

  • A point is an ordered pair of numbers written as (x,y) .
  • Distance is a measure of the length between two points.
  • The formula for finding the distance between any two points is: click here
  • The gradient between two points is determined by the ratio of vertical change to horizontal change.  The formula for finding the gradient of a line is: click here
  •  A straight line is a set of points with a constant gradient between any two of the points. 
  • The standard form of the straight-line equation is y = mx + c
  • The equation of a straight line can also be written as y - y1 = M (x -x1) 
  •  If two lines are parallel, their gradients are equal.
  • If two lines are perpendicular, the product of their gradients is equal to -1 
  • For horizontal lines, the gradient is equal to 0 
  •  For vertical lines, the gradient is undefined.
  • The formula for finding the mid-point between two points is: click here 

Credits

materials are taken from. 

  1. siyavula 
  2. maths is fun 
  3. utube 

Teacher Page

dear student be sure to access all the materials given to be able to master the activity. next week we should be proceeding to the next topic.