Construct and Locate | CSEC Question 3

SHORT TUTORIAL

1
Two points → perpendicular bisector. Two intersecting lines → angle bisectors.
2
Read exactly what is stated. Separate guaranteed facts from appearance.
3
Measure distances to POINTS directly; measure perpendicular distances to LINES.

COACH · ANTICIPATE EACH DECISION

Which tool draws a circular arc of radius 2 cm centred at A?

Before revealing: which property or operation will you use?

Watch for this: An angle bisector and a perpendicular bisector solve different conditions. Preserve the arcs.

MIXED PRACTICE · 8 ITEMS

Practise. Explain. Check.

Show your working or construction on paper. State units where asked. For questions 7 and 8, explain your method. Numerical entries may be rounded to 2 decimal places. Later stages retrieve earlier methods. Answers and explanations stay separate.

Download PDF Open PDF

See answers & explanations

Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.
Compass
A compass keeps the distance from its centre constant.

Self-assess only after at least 7 of 8 independently, including both reasoning items. At stages 4–6, explain a method choice. Before calling the whole skill secure, solve two unseen variants including another context. Repeat after several days. These are teaching targets.

SHORT TUTORIAL

1
Two points → perpendicular bisector. Two intersecting lines → angle bisectors.
2
Choose the operation or construction that matches the condition.
3
Measure distances to POINTS directly; measure perpendicular distances to LINES.

COACH · ANTICIPATE EACH DECISION

Draw equal-radius arcs from the endpoints of a 4 cm segment with radius 3 cm. Join both intersections. Name the constructed line and reproduce it on paper.

Before revealing: which property or operation will you use?

Watch for this: An angle bisector and a perpendicular bisector solve different conditions. Preserve the arcs.

MIXED PRACTICE · 8 ITEMS

Practise. Explain. Check.

Show your working or construction on paper. State units where asked. For questions 7 and 8, explain your method. Numerical entries may be rounded to 2 decimal places. Later stages retrieve earlier methods. Answers and explanations stay separate.

Download PDF Open PDF

See answers & explanations

Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
3 cm
The radius must be greater than half the segment length.
4 cm
The radius must be greater than half the segment length.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.

Self-assess only after at least 7 of 8 independently, including both reasoning items. At stages 4–6, explain a method choice. Before calling the whole skill secure, solve two unseen variants including another context. Repeat after several days. These are teaching targets.

SHORT TUTORIAL

1
Two points → perpendicular bisector. Two intersecting lines → angle bisectors.
2
Choose the operation or construction that matches the condition.
3
Measure distances to POINTS directly; measure perpendicular distances to LINES.

COACH · ANTICIPATE EACH DECISION

A point must be equally distant from two fixed points. Which locus is needed?

Before revealing: which property or operation will you use?

Watch for this: An angle bisector and a perpendicular bisector solve different conditions. Preserve the arcs.

MIXED PRACTICE · 8 ITEMS

Practise. Explain. Check.

Show your working or construction on paper. State units where asked. For questions 7 and 8, explain your method. Numerical entries may be rounded to 2 decimal places. Later stages retrieve earlier methods. Answers and explanations stay separate.

Download PDF Open PDF

See answers & explanations

Perpendicular bisector
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
Angle bisectors
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
Perpendicular bisector
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
Angle bisectors
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
Perpendicular bisector
Each intersection is equidistant from the endpoints; their joining line bisects the segment at 90°.
Perpendicular bisector
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
Angle bisectors
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.

Self-assess only after at least 7 of 8 independently, including both reasoning items. At stages 4–6, explain a method choice. Before calling the whole skill secure, solve two unseen variants including another context. Repeat after several days. These are teaching targets.

SHORT TUTORIAL

1
Two points → perpendicular bisector. Two intersecting lines → angle bisectors.
2
Connect the stated conditions; show each intermediate step and its reason.
3
Measure distances to POINTS directly; measure perpendicular distances to LINES.

COACH · ANTICIPATE EACH DECISION

A point lies on the perpendicular bisector of AB. Its distance to A is 2 cm. Find its distance to B in cm.

Before revealing: which property or operation will you use?

Watch for this: An angle bisector and a perpendicular bisector solve different conditions. Preserve the arcs.

MIXED PRACTICE · 8 ITEMS

Practise. Explain. Check.

Show your working or construction on paper. State units where asked. For questions 7 and 8, explain your method. Numerical entries may be rounded to 2 decimal places. Later stages retrieve earlier methods. Answers and explanations stay separate.

Download PDF Open PDF

See answers & explanations

10
Every point on a perpendicular bisector is equidistant from the two endpoints.
2
Every point on a perpendicular bisector is equidistant from the two endpoints.
3.5
Every point on a perpendicular bisector is equidistant from the two endpoints.
5
Every point on a perpendicular bisector is equidistant from the two endpoints.
Angle bisectors
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
Perpendicular bisector
Equal perpendicular distances to intersecting lines give their angle bisectors; equal distances to points give a perpendicular bisector.
10
Every point on a perpendicular bisector is equidistant from the two endpoints.
2
Every point on a perpendicular bisector is equidistant from the two endpoints.

Self-assess only after at least 7 of 8 independently, including both reasoning items. At stages 4–6, explain a method choice. Before calling the whole skill secure, solve two unseen variants including another context. Repeat after several days. These are teaching targets.

SHORT TUTORIAL

1
Two points → perpendicular bisector. Two intersecting lines → angle bisectors.
2
Connect the stated conditions; show each intermediate step and its reason.
3
Measure distances to POINTS directly; measure perpendicular distances to LINES.

COACH · ANTICIPATE EACH DECISION

A fence must remain equally distant from two intersecting road edges inside their angle. Which single internal locus should it follow?

Before revealing: which property or operation will you use?

Watch for this: An angle bisector and a perpendicular bisector solve different conditions. Preserve the arcs.

MIXED PRACTICE · 8 ITEMS

Practise. Explain. Check.

Show your working or construction on paper. State units where asked. For questions 7 and 8, explain your method. Numerical entries may be rounded to 2 decimal places. Later stages retrieve earlier methods. Answers and explanations stay separate.

Download PDF Open PDF

See answers & explanations

Internal angle bisector
Perpendicular distance to each road edge is equal on their internal angle bisector.
Internal angle bisector
Perpendicular distance to each road edge is equal on their internal angle bisector.
Internal angle bisector
Perpendicular distance to each road edge is equal on their internal angle bisector.
Internal angle bisector
Perpendicular distance to each road edge is equal on their internal angle bisector.
8
Every point on a perpendicular bisector is equidistant from the two endpoints.
10
Every point on a perpendicular bisector is equidistant from the two endpoints.
Internal angle bisector
Perpendicular distance to each road edge is equal on their internal angle bisector.
Internal angle bisector
Perpendicular distance to each road edge is equal on their internal angle bisector.

Self-assess only after at least 7 of 8 independently, including both reasoning items. At stages 4–6, explain a method choice. Before calling the whole skill secure, solve two unseen variants including another context. Repeat after several days. These are teaching targets.

Construct & Locate

Make the relationship visible

Choose and construct bisectors

Check Your Skill Level

Choose and construct bisectors

Practise. Explain. Check.

Practise. Explain. Check.

Practise. Explain. Check.

Practise. Explain. Check.

Practise. Explain. Check.

Practise. Explain. Check.

Use this skill somewhere else

Make the relationship visible

Check Your Skill Level

Choose and construct bisectors

01RecogniseRecognise construction toolsStage 1 of this individual skill

Practise. Explain. Check.

02InterpretInterpret compass arcsStage 2 of this individual skill

Practise. Explain. Check.

03PerformConstruct a basic bisectorStage 3 of this individual skill

Practise. Explain. Check.

04Select & AdaptChoose the correct locusStage 4 of this individual skill

Practise. Explain. Check.

05Connect & JustifyJustify equal distancesStage 5 of this individual skill

Practise. Explain. Check.

06Transfer & SolveLocate a boundary in a planIndependent transfer checkpoint

Practise. Explain. Check.

Use this skill somewhere else