Constructing a right-angled triangle given the length of the hypotenuse and one other side length | Maths

Starter quiz

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

compasses, ruler, protractor and pencil

compasses, protractor and pencil

compasses, ruler and pencil

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

35° ✓

45°

145°

155°
The diagram shows part of a protractor measuring an angle. What is the size of the angle?

67° ✓

73°

113°

127°
Laura is using GeoGebra to accurately draw a triangle with ∠BAC = 135° and ∠ABC = 32° and side AB = 6 units. Which of these tools should Laura use to draw side BC?

a

b

c

d ✓
∠ABC = ______°.

'67' ✓
Starting with the first step, put these instructions in the correct order to construct triangle ABC.

Step 1

⇔

Use a ruler to draw side AB of 6 cm. ✓

Step 2

⇔

Use a protractor to measure 37° from A and mark a faint point. ✓

Step 3

⇔

Repeat the last step with point B and an angle of 40°. ✓

Step 4

⇔

Draw a ray line to show direction of side AC. ✓

Step 5

⇔

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

Step 6

⇔

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

A pair of ______ is a tool which can be used to draw circles and arcs.

'compasses' ✓
Which construction should you use to create a right-angle?

angle bisector

bisector

circle

perpendicular bisector ✓
Jacob is constructing a right-angled triangle and has drawn a line segment for one of its shorter sides. Which tool can be used to construct a perpendicular line through one of its points?

a

b

c ✓

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

'16' ✓
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 = 4 cm; radius of large circle = 7 cm

Radius of small circle = 4 cm; radius of large circle = 14 cm

Radius of small circle = 7 cm; radius of large circle = 8 cm ✓

Radius of small circle = 8 cm; radius of large circle = 14 cm

Radius of small circle = 14 cm; radius of large circle = 16 cm
Starting with the first step, put these instructions in the correct order to construct the triangle ABC where the hypotenuse, AB, is 5 cm and BC is 3 cm.

1

⇔

Open up compasses to 2.5 cm.

2

⇔

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

3

⇔

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

4

⇔

Open up compasses to 3 cm

5

⇔

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

6

⇔

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

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Pupils may want to use a protractor to draw a right angle.

Remind pupils that they need to construct the right angle with a pair of compasses and a ruler, using appropriate construction techniques.

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.