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Construction and Loci — Free MYP5 Mathematics (Standard) Practice Questions
1QuestionConstructing Perpendicular and Angle BisectorsConcept Practice
1 mark~2 minCriterion A
Classify each statement about the angle bisector in the diagram as True or False. Write your answers in the table below.
Angle: ∠AOB = 80°, with ray OC bisecting it, so that ∠AOC = ∠COB = 40°.
Statement Table:
Angle: ∠AOB = 80°, with ray OC bisecting it, so that ∠AOC = ∠COB = 40°.
Statement Table:
| Statement | ∠AOC = ∠COB | ∠AOB = 2 × ∠AOC | ∠AOB = ∠AOC | ∠COB = 40° |
|---|---|---|---|---|
| Classification | True or False | True or False | True or False | True or False |
Solutions
2QuestionConstructing Perpendicular and Angle BisectorsAssessment Practice
3 marks~5 minCriterion B
Investigate whether the angle bisectors of the interior angles of a regular polygon always intersect at a single point. Consider a regular pentagon (5 sides), a regular hexagon (6 sides), and a regular heptagon (7 sides). For each polygon, draw the angle bisectors of all interior angles.
a
For the regular pentagon, do the angle bisectors all meet at one point? If yes, describe that point's location relative to the polygon.
b
Based on the results for the pentagon, hexagon, and heptagon, state a general rule about the angle bisectors of any regular polygon.
c
Test your rule by predicting whether the angle bisectors of a regular octagon (8 sides) will all intersect at a single point. Explain your reasoning.
Solutions
3QuestionConstructing Perpendicular and Angle BisectorsAssessment Practice
4 marks~6 minCriterion C
Consider a line segment drawn on a grid.
Explain, step-by-step, how to construct the perpendicular bisector of line segment using a compass and straightedge. Your explanation must include:
Explain, step-by-step, how to construct the perpendicular bisector of line segment using a compass and straightedge. Your explanation must include:
a
A sketch of the construction, clearly labeling points , , , , and , where and are the intersection points of the arcs, and is the midpoint of .
b
A detailed written description of each step in the construction, including the compass settings used in each step.
c
A justification for why the line segment is the perpendicular bisector of , referring to properties of congruent triangles.
Solutions
4QuestionConstructing Perpendicular and Angle BisectorsAssessment Practice
6 marks~9 minCriterion D
Landscape designer Zara is planning a garden path that must be equidistant from two fixed points, and , marked on a scale drawing. The line segment is drawn below.
a
Construct the perpendicular bisector of using a compass and straightedge only. All construction arcs must be visible. [2]
b
Label a point on the perpendicular bisector. Measure and record the distances and in centimetres. [1]
c
Calculate the percentage difference between and using:
[1]
[1]
d
Zara's design specification states the path must be within 5\% of equidistant from and to be approved. Advise Zara whether her construction meets the specification, and explain what any deviation from 0\% reveals about the accuracy of the compass-and-straightedge method. [2]
Solutions
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