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Year 11
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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.

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New
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Year 11
Higher

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.

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Lesson details

Key learning points

  1. The first side can be drawn accurately with a ruler
  2. All triangles with these measurements in the same place are congruent
  3. The angle should be accurately measured with a protractor
  4. 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 (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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Starter quiz

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6 Questions

Q1.
A pair of compasses is a tool which can be used to draw __________ and __________.
angles
Correct answer: arcs
Correct answer: circles
rays
segments
Q2.
To create a right-angle you can construct a bisector.
Correct Answer: perpendicular
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?
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a
Correct answer: b
c
d
Q4.
The diagram shows a right-angled triangle constructed from two circles. The length of the hypotenuse is cm.
An image in a quiz
Correct Answer: 14
Q5.
The diagrams below show constructions for two congruent triangles. What is the radius of each circle in the diagram on the right?
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Radius of small circle = 3 cm; radius of large circle = 5 cm
Radius of small circle = 3 cm; radius of large circle = 10 cm
Correct answer: Radius of small circle = 5 cm; radius of large circle = 6 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.
An image in a quiz
Correct Answer:Step 1,Open up compasses to 6.5 cm.

Open up compasses to 6.5 cm.

Correct Answer:Step 2,Mark a centre point and use compasses to draw a circle.

Mark a centre point and use compasses to draw a circle.

Correct Answer:Step 3,Use a ruler to draw the diameter, AB, of the circle.

Use a ruler to draw the diameter, AB, of the circle.

Correct Answer:Step 4,Open up compasses to 5 cm.

Open up compasses to 5 cm.

Correct Answer:Step 5,Put compass needle at B and draw a 2nd circle.

Put compass needle at B and draw a 2nd circle.

Correct Answer:Step 6,Label one point where circles intersect C, and draw lines AC and BC.

Label one point where circles intersect C, and draw lines AC and BC.

Exit quiz

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6 Questions

Q1.
Which angle is 48°?
An image in a quiz
∠ACB
Correct answer: ∠BAC
∠CBA
Q2.
Match the tools with what they are useful for when constructing a triangle.
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Correct Answer:Tool a,Finding all possible positions for a vertex when drawing a 2nd side

Finding all possible positions for a vertex when drawing a 2nd side

Correct Answer:Tool b,Drawing an angle to show what direction a side takes

Drawing an angle to show what direction a side takes

Correct Answer:Tool c,Drawing the first side of a triangle

Drawing the first side of a triangle

Q3.
Match each triangle to the type of triangle it is.
An image in a quiz
Correct Answer:A,SSS

SSS

Correct Answer:B,SAS

SAS

Correct Answer:C,SSA

SSA

Correct Answer:D,RHS

RHS

Correct Answer:E,ASA

ASA

Q4.
Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join Q to?
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R only
S only
Correct answer: R and S
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?
Correct answer: Triangle 1: ASA
Correct answer: Triangle 2: RHS
Correct answer: Triangle 3: SAS
Triangle 4: SSA
Correct answer: Triangle 5: SSS
Q6.
Starting with the first step, put these instructions in the correct order to construct the triangle PQR.
An image in a quiz
1 - Use a ruler to draw side PQ.
2 - Set compasses to 6 cm and draw a circle centre Q.
3 - Draw a ray line at angle of 42° at P.
4 - Mark R at the point(s) where the ray and circle meet.
5 - Add the line(s) RQ to complete the triangle(s).