8.16 Constructions

Describe how to measure an angle using a protractor.

A protractor reading is 130°. Identify whether the angle is acute, right, obtuse, or reflex.

Construct an angle of 60° using a compass on a starting line. Describe the steps.

Describe how to copy a given line segment using a compass and straight-edge.

A right angle is what number of degrees? Describe how to construct a perpendicular through a point on a line.

Construct an equilateral triangle on a given segment AB using compass and straightedge. Describe the construction.

Sketch and describe how to bisect a line segment AB using compass and ruler.

The "seed of life" is a classical construction. Describe it.

Sketch the inscribed regular hexagon in a circle. Why does the construction work?

Use compass and ruler to construct a 30° angle. Describe.

Construct a triangle with sides 5 cm, 6 cm, 7 cm using compass and ruler.

Bisect an angle of 80°. Describe the steps and find the resulting angle.

Construct a 45° angle.

Construct a triangle with sides 6 cm, 6 cm, 6 cm. What type of triangle is this?

Construct a regular hexagon inscribed in a circle of radius 4 cm.

A perpendicular bisector of segment AB passes through the midpoint and is at 90° to AB. Why is every point on this bisector equidistant from A and B?

Construct a square of side 5 cm.

Construct a 15° angle. Describe.

Why can a 60° angle be constructed but not a 20° angle with compass and straightedge only?

A construction involves "marking and arc". Describe the difference between drawing an arc and a full circle.

Construct an isosceles triangle with base 6 cm and equal sides 5 cm each. Calculate the height from apex to base.

A right-angled triangle has legs 3 and 4. Construct it and verify the hypotenuse using Pythagoras.

Construct the perpendicular bisector of a 10 cm segment. Verify that midpoint is 5 cm from each endpoint and the bisector is at 90°.

Construct a regular pentagon inscribed in a circle. (Outline the steps for the standard ruler-and-compass construction.)

A 75° angle can be constructed as 60° + 15° (or 45° + 30°). Describe both methods.

Construct the seed-of-life flower (7 interlocking circles). Describe the procedure and the angles created at the centres.

A regular hexagon has side 8 cm. Find (a) the radius of the inscribed circle (apothem) and (b) the radius of the circumscribed circle.

Construct a parallel to a given line through an external point. Describe.

Construct a triangle with sides 5, 5, 5 cm. Find the area without measuring (use Pythagoras to find the height).

A protractor reading of 47° is given. Construct (without protractor!) an angle of 47° approximately — list approximate methods and their limits.

Construct an equilateral triangle on a given segment AB, then construct its **circumscribed circle** (passing through all three vertices).

Describe how to construct a regular pentagon with side 5 cm using only ruler and compass.

Verify the "seed of life" structure: six surrounding circles in a hexagonal pattern. Why is this geometric arrangement special?

Construct a triangle with sides 7 cm, 8 cm, 9 cm. Calculate its area using Heron's formula.

A complex construction: starting from an equilateral triangle ABC, construct the perpendicular from one vertex to the opposite side. What is the relationship between this perpendicular and the median?

Trisect a 90° angle — is this possible using only compass and straightedge?

Construct a regular hexagon with apothem 4 cm. Find the side length.

Construct a triangle similar to a given triangle with sides 3, 4, 5 cm, but with a linear scale factor of 1.5.

Construct an inscribed regular dodecagon (12-gon) in a circle. Outline the procedure.

In a circle of radius 5 cm, construct an isosceles trapezium with parallel sides 6 cm and 8 cm.