Constructions Flashcards

All 5 cards in this deck

What are the steps to construct the perpendicular bisector of a line segment?
e.g. the line segment $AB$

1. Open compasses to more than half of $AB$; draw arcs above and below from $A$.
2. Keeping the same radius, draw arcs from $B$ to cross them.
3. Join the two crossing points — this line cuts $AB$ in half at $90°$.

What are the steps to construct the bisector of an angle?
e.g. the bisector of angle $ABC$

1. With compasses centred on $B$, draw an arc crossing both arms.
2. From each crossing point, draw equal arcs that intersect.
3. Join $B$ to that intersection — it splits the angle in two.

What are the steps to construct the perpendicular from a point to a line, using ruler and compasses?
e.g. from point $P$ to the line $CD$

1. With compasses centred on $P$, draw an arc crossing $CD$ twice.
2. From each of those two points, draw equal arcs that meet on the other side of $CD$.
3. Join $P$ to that intersection.

What are the steps to construct an angle of $90°$ at a point on a line?
e.g. at the point $P$ on the line $AB$

1. With compasses centred on $P$, mark equal distances either side of $P$ on the line.
2. From each of those two marks, draw larger equal arcs that cross above the line.
3. Join $P$ to that crossing point.

What is the shortest distance from a point to a line?

The perpendicular distance from the point to the line.