Constructing a triangle given two side lengths and an angle not between them | Maths

Starter quiz

A pair of compasses is a tool which can be used to draw __________ and __________.

angles

arcs ✓

circles ✓

rays

segments
To create a right-angle you can construct a ______ bisector.

'perpendicular' ✓
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

b ✓

c

d
The diagram shows a right-angled triangle constructed from two circles. The length of the hypotenuse is ______ cm.

'14' ✓
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 = 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
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.

Step 1

⇔

Open up compasses to 6.5 cm. ✓

Step 2

⇔

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

Step 3

⇔

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

Step 4

⇔

Open up compasses to 5 cm. ✓

Step 5

⇔

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

Step 6

⇔

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

Which angle is 48°?

∠ACB

∠BAC ✓

∠CBA
Match the tools with what they are useful for when constructing a triangle.

Tool a

⇔

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

Tool b

⇔

Drawing an angle to show what direction a side takes ✓

Tool c

⇔

Drawing the first side of a triangle ✓
Match each triangle to the type of triangle it is.

A

⇔

SSS ✓

B

⇔

SAS ✓

C

⇔

SSA ✓

D

⇔

RHS ✓

E

⇔

ASA ✓
Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join Q to?

R only

S only

R and S ✓

Midpoint of R and S
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 1: ASA ✓

Triangle 2: RHS ✓

Triangle 3: SAS ✓

Triangle 4: SSA

Triangle 5: SSS ✓
Starting with the first step, put these instructions in the correct order to construct the triangle PQR.

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).

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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.

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.