Constructing loci | Maths | Quizalize & Oak National Academy

Starter quiz

Which angle is 52°?

∠PQR

∠RPQ ✓

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

compasses

⇔

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

protractor

⇔

Drawing an angle to show what direction a side takes ✓

ruler

⇔

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

A

⇔

RHS ✓

B

⇔

SAS ✓

C

⇔

SSA ✓

D

⇔

ASA ✓

E

⇔

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

C only

D only

C and D ✓

Midpoint of C and D
The following information is given for five different triangles. Jun and Sam both accurately construct each triangle. Which triangle information may not produce 2 congruent triangles?

Triangle 1: ASA

Triangle 2: RHS

Triangle 3: SAS

Triangle 4: SSA ✓

Triangle 5: SSS
Match each step to the correct instruction in order to construct the triangle PQR.

Step 1:

⇔

Use a ruler to draw side PQ. ✓

Step 2:

⇔

Set compasses to 7 cm and draw a circle centre Q. ✓

Step 3:

⇔

Draw a ray line at angle of 45° at P. ✓

Step 4:

⇔

Mark R at the point(s) where the ray and circle meet. ✓

Step 5:

⇔

Add the line(s) RQ to complete the triangle(s). ✓

Exit quiz

A ______ is a set of points that satisfy a given set of conditions.

'locus' ✓
Which diagram shows the locus of points exactly 2 metres from point P?

Diagram a ✓

Diagram b

Diagram c

Diagram d
Which diagram shows the locus of points less than 2 metres from point P?

Diagram a

Diagram b

Diagram c ✓

Diagram d
Which diagram shows the locus of points 5 metres or more from the line segment PQ?

Diagram a

Diagram b ✓

Diagram c

Diagram d
Which diagram shows the locus of points less than 5 metres from the line segment PQ?

Diagram a

Diagram b

Diagram c

Diagram d ✓
Izzy stands somewhere in her garden. Izzy is less than 5 m from the house and less than 6 m from the tap. She is within 3 m of the tree. Izzy is standing in region ______.

'F' ✓

Worksheet

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Lesson Details

Key learning points

Constructing a set of points a set distance from a given point produces a circle
A compass should be used for this construction
The point could be the vertex of a shape or contained within a shape
A ruler should be used to indicate two points that are a set distance from a line
The end points of the line should have a compass used to indicate the distance from the point

Common misconception

Pupils may think that the locus of a line is a rectangle.

Choose the vertices of their rectangle and ask if they are the same distance from the line as another point. Link to Pythagoras' theorem if necessary to highlight that the diagonal length will be longer.

Keywords

Locus/loci - A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
Circle - A circle is a locus of points that are equidistant from a fixed point. This fixed point is the centre of the circle and the distance from the centre to the locus of points is the radius of the circle.