equal lengths can be established from the diagonals of rectangles (or, later, by pythagoras)
a powerpoint is here
show that the diagonals of kites cross at right angles
Showing posts with label perpendicular lines. Show all posts
Showing posts with label perpendicular lines. Show all posts
Friday, 6 March 2020
grid geometry perpendiculars
it seems helpful to consider (and then define) perpendicularity in terms of a 'rotated' vector (through 90 degrees)
equal lengths can be established from the diagonals of rectangles (or, later, by pythagoras)
a powerpoint is here
show that the diagonals of kites cross at right angles
equal lengths can be established from the diagonals of rectangles (or, later, by pythagoras)
a powerpoint is here
show that the diagonals of kites cross at right angles
Tuesday, 5 February 2019
GCSE line questions
these are based on recent Edexcel questions
they involve finding perpendiculars
the powerpoint is here
they involve finding perpendiculars
the powerpoint is here
Thursday, 23 November 2017
two tangents meet on the y-axis
these tasks are my versions of a five triangles tweeted task (on July 19th 2017)
their tweets are now protected
their tweets are now protected
Friday, 11 November 2016
trapezium area bisected
intended to practice using a method for calculating the area of a trapezium
the powerpoint is here
the space underneath each shape is for students to record (show) their calculations
the shapes should be congruent:
creating half of the trapeziums has an easily spotted rule
why does this rule work?
this offers an introduction to perpendicular gradients (or rotations of 90 degrees)
the powerpoint is here
the space underneath each shape is for students to record (show) their calculations
the shapes should be congruent:
why does this rule work?
this offers an introduction to perpendicular gradients (or rotations of 90 degrees)
Thursday, 20 October 2016
triangles cut into triangles
the main purpose of this work is to provide a focus on triangle areas
particularly with same bases and equal heights (Euclid I. 37)
but there are various optional spin-offs:
questions for the triangles above
the team at Puntmat (@puntmat) have found 8 ways (so far) to cut up a 3 by 6 right triangle into three equal areas (i.e. non-congruent thirds):
their post on fractions of geometrical shapes contains many good exercises
many thanks to them
dividing unequally:
particularly with same bases and equal heights (Euclid I. 37)
but there are various optional spin-offs:
- perpendicular lines
- surd lengths
- length and area ratios of similar shapes
their post on fractions of geometrical shapes contains many good exercises
many thanks to them
dividing unequally:
Thursday, 31 March 2016
quadratic graph properties
some of the properties of y = x ^ 2
only considering integer points
work developed with David Wells
a ppt is here
several interesting applications of:
only considering integer points
work developed with David Wells
a ppt is here
several interesting applications of:
- straight line graphs (the chord equations are all neat)
- mid-points
- tangents (are parallel to a family of chords)
- perpendicular line equations
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