Exercises and resolutions

Exercise 1 — Classify as true (V) or false (F)

  1. An infinite number of straight lines pass through a point.
  2. A straight line passes through two distinct points.
  3. A straight line contains two distinct points.
  4. Two distinct points determine one and only one straight line.
  5. A single straight line passes through three given points.

Exercise 2 — Classify as true (V) or false (F)

  1. Three distinct points are always collinear.
  2. Three distinct points are always coplanar.
  3. Four distinct points determine two straight lines.
  4. A single straight line can pass through four distinct points.
  5. Three points belonging to a plane are always collinear.

Exercise 3 — Classify as true (V) or false (F)

  1. Whatever the points $A$ and $B$, if $A$ is distinct from $B$, then there is a straight line $a$ such that $A \in a$ and $B \in a$.
  2. Whatever the points $P$ and $Q$ and the lines $r$ and $s$, if $P \neq Q$ and $P$ and $Q$ belong to $r$ and $s$, then $r = s$.
  3. Whatever the straight line $r$, there are two points $A$ and $B$ such that $A \neq B$, with $A \in r$ and $B \in r$.
  4. If $A = B$, there is a straight line $r$ such that $A, B \in r$.
4

Using four distinct points, three of which are collinear, how many straight lines can we construct? Try the “4 points, 3 collinear” button in the points figure.

Ver resposta

4 straight lines. The three collinear points determine a single straight line; the fourth point forms a straight line with each of them: $1 + 3 = 4$.

Exercise 5 — Classify as true (V) or false (F)

  1. Two distinct lines that have a common point are concurrent.
  2. Two competing straight lines have a common point.
  3. If two distinct lines have a common point, then they have a single common point.