JHS2 Mathematics · Term 3, Week 1

Shapes and Space

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Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.

Curriculum details

Strand
Geometry and Measurement (Strand 3)
Sub-strand
Shapes and Space (3.1)
Content standard
B8.3.1.2 - Demonstrate the ability to perform geometric constructions of the angles (75˚, 105˚, 60˚, construct triangles and find locus of points under given conditions.
Indicator
B8.3.1.2.3 - Construct loci under given conditions including: (i) the locus of sets of points from a fixed point; (ii) the locus of points equidistant from two fixed points; (iii) the locus of points equidistant from two intersecting straight lines, (iv) the locus of points equidistant from two parallel lines.
Suggested placement
Term 3, Week 1 (Week 25 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Curriculum reference
Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 133

Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1: Describe the locus of a circle by tracing the path of a point P which moves in such a way that its distance from a fixed point, say O, is always the same to construct circles.
Figure from the jhs2 mathematics curriculum, printed page 133
E.g.2: Perform geometric construction to locate the centre of a circle by locating the intersection of the perpendicular bisectors of any two chords on the circle.
Figure from the jhs2 mathematics curriculum, printed page 134
E.g.3: Draw circles of given radii at the points as centre and chord.
Figure from the jhs2 mathematics curriculum, printed page 135
E.g.4: Construct a regular hexagon within a circle given the length of a side Use a pair of compasses and a ruler to construct a hexagon ABCDEF such that |AB| = 6cm. Find the measure of the angles AOB and compare to its value to ∠AFG, ∠DOE, ∠DOC, ∠EOF and ∠BOC. What is your observation?
Figure from the jhs2 mathematics curriculum, printed page 136
E.g.5 Use intersecting circles to construct a regular hexagon and measure it sides. Perform geometric construction of hexagon ABCDEF using the method of intersecting circles. Take |OA| = 5cm. Measure and compare the sides of the hexagon. Find the measure of the angles AOB and compare to its value to ∠AFG, ∠DOE, ∠DOC, EOF and ∠BOC. What is your observation?
Figure from the jhs2 mathematics curriculum, printed page 137
E.g.6: Construct a perpendicular bisector (mediator) as a locus and explain why the perpendicular bisector is a locus.
The line segment AB is a perpendicular bisector of PQ since line segments AP, AQ, PB, QB are all congruent.
Figure from the jhs2 mathematics curriculum, printed page 138
Any point on line CD is of equal distance from the two fixed points A and B.
Figure from the jhs2 mathematics curriculum, printed page 139
E.g. 7 Construct an angle bisector as a locus of points equidistant from two lines that meet and explain why the angle bisector is a locus.
Figure from the jhs2 mathematics curriculum, printed page 140
E.g.8: Construct parallel lines as a locus (i.e. tracing the path of a point say P which moves in such a way that its distance from line BC is always the same).
Figure from the jhs2 mathematics curriculum, printed page 141
E.g.9: Perform geometric constructions to prove that two given lines are parallel. Show that two given lines AB and CD are parallel (i.e. locate three points P, Q and R) draw perpendicular to AB at PQ and R to intersect CD at E, F and G respectively.
Figure from the jhs2 mathematics curriculum, printed page 141
Measure the lengths of PE, QF, and RG. The perpendicular distance between two parallel lines is the same everywhere.