New
New
Constructing a triangle given two side lengths and an angle not between them
I can construct a triangle from two side lengths and an angle not between them.
Lesson 9 of 13
New
New
- Year 11
Constructing a triangle given two side lengths and an angle not between them
I can construct a triangle from two side lengths and an angle not between them.
Lesson details
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.
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.
Teacher tip
Equipment
Pair of compasses, protractor, ruler
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
Loading...
Prior knowledge starter quiz
6 Questions
Q1.A pair of compasses is a tool which can be used to draw __________ and __________.
A pair of compasses is a tool which can be used to draw __________ and __________.
angles
rays
segments
Q2.To create a right-angle you can construct a bisector.
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?
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?
a
c
d
Q4.The diagram shows a right-angled triangle constructed from two circles. The length of the hypotenuse is cm.
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?
The diagrams below show constructions for two congruent triangles. What is the radius of each circle in the diagram on the right?
Radius of small circle = 3 cm; radius of large circle = 5 cm
Radius of small circle = 3 cm; radius of large circle = 10 cm
Radius of small circle = 3 cm; radius of large circle = 6 cm
Radius of small circle = 6 cm; radius of large circle = 10 cm
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.
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.
Assessment exit quiz
6 Questions
Q1.Which angle is 48°?
Which angle is 48°?
∠ACB
∠CBA
Q2.Match the tools with what they are useful for when constructing a triangle.
Match the tools with what they are useful for when constructing a triangle.
Q3.Match each triangle to the type of triangle it is.
Match each triangle to the type of triangle it is.
Q4.Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join Q to?
Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join Q to?
R only
S only
Midpoint of R and S
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?
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?
Triangle 4: SSA
Q6.Starting with the first step, put these instructions in the correct order to construct the triangle PQR.
Starting with the first step, put these instructions in the correct order to construct the triangle PQR.
