Exercises: Constructions 4 to 15

Using only a compass and straight edge, draw a line segment $[AB]$ of length $7 \text{ cm}$. Construct the perpendicular bisector of $[AB]$ and state which construction number this is.

Draw a line $\ell$ and mark a point $P$ not on $\ell$. Construct the line through $P$ perpendicular to $\ell$, using a compass and straight edge.

Using a compass and straight edge, construct an angle of $60^\circ$ and then bisect it. State the size of each resulting angle.

Draw a line $\ell$ and mark a point $P$ not on $\ell$. Construct the line through $P$ parallel to $\ell$. Describe the steps you used.

Construct triangle $ABC$ with $AB = 6 \text{ cm}$, $BC = 5 \text{ cm}$ and $AC = 4 \text{ cm}$. Measure angle $B$ and state its size to the nearest degree.

Construct triangle $PQR$ with $PQ = 7 \text{ cm}$, angle $P = 50^\circ$ and angle $Q = 70^\circ$. Calculate angle $R$ and verify by measuring.

Construct a right-angled triangle $ABC$ with hypotenuse $AC = 9 \text{ cm}$ and one other side $AB = 5 \text{ cm}$.

1. a) Describe the steps of your construction.
2. b) Use Pythagoras' theorem to calculate $BC$ and check by measurement.

Construct a rectangle $ABCD$ with $AB = 8 \text{ cm}$ and $BC = 5 \text{ cm}$ using only a compass and straight edge.

1. a) Describe your steps.
2. b) Explain why the figure you drew is a rectangle, using properties of perpendicular and parallel lines.

Construct a triangle $ABC$ with $AB = 6 \text{ cm}$, angle $A = 45^\circ$ and $AC = 7 \text{ cm}$. Then construct the line through $C$ parallel to $AB$ and the line through $B$ perpendicular to $AC$.

1. a) Describe your steps.
2. b) Measure the distance from $C$ to $AB$ and verify it using trigonometry.