Constructing a triangle given two side lengths and an angle not between them
Lesson details
Learning outcome
I can construct a triangle from two side lengths and an angle not between them.
Key learning points
- The first side can be drawn accurately with a ruler
- All triangles with these measurements in the same place are congruent
- The angle should be accurately measured with a protractor
- Two different triangles can be drawn with these measurements
Keywords
Pair of compasses - A pair of compasses is a tool which can be used to draw circles and arcs. A pair of compasses is sometimes referred to just as a compass.
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Common misconception
Pupils may not use a pair of compasses to find the two positions of the third vertex and instead just try to use their ruler.
You could encourage them to draw the circle before the angle each time.
Teacher tip
Remind pupils that SSA is not a condition for proving congruency in triangles, as two possible different triangles can be created using this information. This can be linked to solving angle problems using the sine rule.
Equipment
Pair of compasses, protractor, ruler
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A pair of compasses is a tool which can be used to draw __________ and __________.
Q2.To create a right-angle you can construct a bisector.
Q3.Alex is constructing a right-angled triangle and has drawn a line segment. Which tool can be used to construct the perpendicular bisector of his line?
Q4.The diagram shows a right-angled triangle constructed from two circles. The length of the hypotenuse is cm.
Q5.The diagrams below show constructions for two congruent triangles. What is the radius of each circle in the diagram on the right?
Q6.Match each step to the correct instruction in order to construct the triangle ABC where the hypotenuse, AB, is 13 cm and BC is 5 cm.
Open up compasses to 6.5 cm.
Mark a centre point and use compasses to draw a circle.
Use a ruler to draw the diameter, AB, of the circle.
Open up compasses to 5 cm.
Put compass needle at B and draw a 2nd circle.
Label one point where circles intersect C, and draw lines AC and BC.
Assessment exit quiz
6 Questions
Q1.Which angle is 48°?
Q2.Match the tools with what they are useful for when constructing a triangle.
Finding all possible positions for a vertex when drawing a 2nd side
Drawing an angle to show what direction a side takes
Drawing the first side of a triangle
Q3.Match each triangle to the type of triangle it is.
SSS
SAS
SSA
RHS
ASA
Q4.Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join Q to?
Q5.The following information is given for five different triangles. Alex and Sam both accurately construct each triangle. Which triangle information will definitely produce 2 congruent triangles?
Q6.Starting with the first step, put these instructions in the correct order to construct the triangle PQR.
To help you plan your 11 maths lesson on: Constructing a triangle given two side lengths and an angle not between them, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 11 maths lesson on: Constructing a triangle given two side lengths and an angle not between them, 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.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Loci and construction unit, dive into the full secondary maths curriculum, or learn more about lesson planning.