Checking and securing understanding of constructing a perpendicular to a given line through a point
I can use the properties of a rhombus to construct a perpendicular to a given line through a given point.
Checking and securing understanding of constructing a perpendicular to a given line through a point
I can use the properties of a rhombus to construct a perpendicular to a given line through a given point.
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Lesson details
Key learning points
- A rhombus can be constructed from two congruent isosceles triangles.
- This can be used to construct a perpendicular to a line through a point.
- This perpendicular has special properties that can be investigated.
- The line and point could be part of a shape.
Keywords
Bisect - To bisect means to cut or divide an object into two equal parts.
Rhombus - A rhombus is a parallelogram where all sides are the same length.
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Common misconception
"My construction didn't accurately bisect the line segment"
Check that your compasses construct a full circle, and do not slip (and create a spiral-shape). Tighten the screw on your compasses, if possible. Then, if only using construction arcs that look confusing, you can construct full circles to help.
To help you plan your year 11 maths lesson on: Checking and securing understanding of constructing a perpendicular to a given line through a point, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Checking and securing understanding of constructing a perpendicular to a given line through a point, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
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The assessment exit quiz will test your pupils' understanding of the key learning points.
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Equipment
Pair of compasses, protractor, ruler.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.To bisect means to cut or divide an object into equal parts.
Q2.Which of these is not a property of any rhombus?
Q3.Two triangles are put together to form a quadrilateral. Which quadrilateral is a rhombus?
Q4.Aisha correctly draws three of the four arcs needed to construct the perpendicular bisector of LM. Point A is 6 cm away from point L. Point B is cm away from point M.
Q5.Lucas correctly draws three of the four arcs needed to construct the perpendicular bisector of AB. Point C is from A and B.
Q6.Which of these diagrams show an accurate construction of a perpendicular bisector of the line segment PQ?
Assessment exit quiz
6 Questions
Q1.A perpendicular to the line AB is a line that is at an angle of ° to AB.
Q2.Sam has incorrectly constructed a perpendicular for LM through P. What is wrong with Sam's construction?
Q3.Which of these circles will help in the construction of the perpendicular to AB through point P.
Q4.Jun has partially completed a construction for a perpendicular of QR through P. What is incorrect about Jun’s pair of compasses?
Q5.The diagram shows the perpendicular through Z to the line segment SR. The shortest distance from Z to an extension of line segment SR is cm.
Q6.The diagram shows the perpendicular through Z to the line segment SR. The shortest distance from Z to the original line segment SR is cm.