New
New
Year 11
Higher

Constructing a triangle given two side lengths and the angle between them using a compass

I can construct a triangle given two of the required side lengths and the size of the angle between them.

New
New
Year 11
Higher

Constructing a triangle given two side lengths and the angle between them using a compass

I can construct a triangle given two of the required side lengths and the size of the angle between them.

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Lesson details

Key learning points

  1. The first side can be drawn accurately with a ruler
  2. The compass should be used to indicate potential positions for the remaining side
  3. A protractor should be used to accurately measure the desired angle
  4. The line to mark the required angle should be drawn to meet one of the potential positions for the remaining side
  5. All triangles with the same measurements are congruent

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

Some pupils may not recognise that they have constructed congruent triangles to one and another.

Use a piece of tracing paper to show that the triangles are congruent to each other.

To check the accuracy of the pupil's work, either use a tracing paper overlay or have pupils use the cosine rule to calculate the third edge and measure with a ruler.
Teacher tip

Equipment

Pair of compasses, ruler and protractor

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Andeep sets his compasses to the width shown in the diagram. Without changing the setting, Andeep draws a circle. The diameter of the circle is cm.
An image in a quiz
Correct Answer: 10
Q2.
What equipment do you need in order to accurately construct a perpendicular bisector?
A calculator
Correct answer: A pair of compasses
A protractor
Correct answer: A ruler
Correct answer: A sharp pencil
Q3.
Sofia is using GeoGebra to accurately draw a triangle with side lengths 6 units, 8 units and 10 units. Which of these tools should Sofia use to find the points where her two circles intersect?
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Correct answer: a
b
c
d
Q4.
Lucas and Sofia both accurately construct triangles of sides 8 cm, 9 cm and 11 cm. Which statement is correct?
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The triangles are definitely similar.
Correct answer: The triangles are definitely congruent.
The triangles are neither similar nor congruent.
The triangles could be congruent, but the angles need to be checked to be sure.
Q5.
Here are two circles with centres A and B. The circles meet at C and D. The radius of the circles are 8.5 cm and 9.6 cm. The distance between their centres is 7.3 cm. Match each length to its value.
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Correct Answer:AB,7.3 cm

7.3 cm

Correct Answer:CB,9.6 cm

9.6 cm

Correct Answer:AD,8.5 cm

8.5 cm

Q6.
Match each step to the correct instruction needed to construct a triangle ABC with sides 5 cm, 6 cm and 7 cm.
Correct Answer:Step 1,Use a ruler to draw line of length 5 cm. Label line A and B

Use a ruler to draw line of length 5 cm. Label line A and B

Correct Answer:Step 2,Set compasses to 6 cm and needle of compasses on A.

Set compasses to 6 cm and needle of compasses on A.

Correct Answer:Step 3,Draw a circle of radius 6 cm, centre A.

Draw a circle of radius 6 cm, centre A.

Correct Answer:Step 4,Repeat last 2 steps using B and 7 cm.

Repeat last 2 steps using B and 7 cm.

Correct Answer:Step 5,Label one of the points where the 2 circles intersect as C.

Label one of the points where the 2 circles intersect as C.

Correct Answer:Step 6,Use a ruler to join both A and B to C.

Use a ruler to join both A and B to C.

6 Questions

Q1.
The diagram shows part of a protractor measuring an angle. What is the size of the angle?
An image in a quiz
Correct answer: 68°
72°
112°
128°
Q2.
The diagram shows a protractor measuring an angle. What is the size of the angle?
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64°
76°
Correct answer: 116°
124°
Q3.
Jacob is using GeoGebra to accurately draw a triangle with side lengths 8 units, 9 units and an angle of size 67° between them. Which tool should Jacob use to construct the angle?
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Correct answer: a
b
c
d
Q4.
A pair of compasses is used to draw an arc. The value of $$x$$ is .
An image in a quiz
Correct Answer: 9, 9 cm, 9cm
Q5.
Jun draws a ray line and a circle with radius 5 units then marks their intersection with point C. Which line segment has a length of 5 units?
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Correct Answer: AC, CA
Q6.
Starting with the first step, put these instructions in the correct order to construct triangle ABC.
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1 - Use a ruler to draw side AC of 9 cm.
2 - Use a protractor to measure 48° at A and mark a faint point.
3 - Draw a ray line through A to show direction of AB.
4 - Set compasses to width of 8 cm and mark an arc on the ray.
5 - Label point where arc meets the ray as B.
6 - Use a ruler to connect C and B.