Constructing a triangle given two angles and the side length between them | Maths

Starter quiz

The diagram shows part of a protractor measuring an angle. What is the size of the angle?

72° ✓

88°

108°

112°
The diagram shows a protractor measuring an angle. What is the size of the angle?

56°

64°

124° ✓

136°
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 a ray line?

a

b

c

d ✓
A pair of compasses is used to draw an arc. The value of $x$ is ______.

'11' ✓
Laura draws a ray line and a circle with radius 10 units then marks their intersection with point C. Which line segment has a length of 10 units?

'AC' ✓
Match each step to the correct instruction needed to construct triangle ABC.

Step 1

⇔

Use a ruler to draw side AC of 7 cm. ✓

Step 2

⇔

Use a protractor to measure 52° at A and mark a faint point. ✓

Step 3

⇔

Draw a ray line through A to show direction of AB. ✓

Step 4

⇔

Set compasses to width of 9 cm and mark an arc on the ray. ✓

Step 5

⇔

Label point where arc meets the ray as B. ✓

Step 6

⇔

Use a ruler to connect C and B. ✓

What equipment should you use to make an accurate construction of this triangle?

a pair of compasses

a protractor ✓

a rubber to rub out all construction lines

a ruler ✓

a sharp pencil ✓
The diagram shows part of a protractor measuring an angle. What is the size of the angle?

78° ✓

82°

102°

118°
The diagram shows part of a protractor measuring an angle. What is the size of the angle?

15° ✓

25°

165°

175°
Laura is using GeoGebra to accurately draw a triangle with ∠BAC = 125° and ∠ABC = 32° and side AB = 5 units. Which tool should Laura use to plot point C?

a

b

c ✓

d
∠ABC = ______°.

'76' ✓
Match each step to the correct instruction needed to construct triangle ABC.

1

⇔

Use a ruler to draw side AB of 7 cm.

2

⇔

Use a protractor to measure 38° from A and mark a faint point.

3

⇔

Repeat the last step with point B and an angle of 43°.

4

⇔

Draw a ray line to show direction of side AC.

5

⇔

Draw a second ray line to show direction of side BC.

6

⇔

Label point C at the point where the two rays meet.

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The side can be drawn accurately with a ruler
Both angles should be accurately measured with a protractor
Where the lines marking each angle intersect is where the lines should be drawn to
All triangles with the same measurements are congruent

Pupils may struggle to spot congruent triangles if they only look for ASA (angle-side-angle).

Encourage pupils to add any further information to diagrams, like the third angle, before starting to prove congruence.

Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.