Coaching Centre
Transversals and parallel lines
Corresponding, alternate and co-interior angles formed when a transversal crosses parallel lines, and how to prove lines are parallel.
Angle pairs on parallel lines
A transversal is a line that crosses two or more other lines. When the lines are parallel, special pairs of angles are related.
Both parallel lines meet the transversal at the same angle. That is why corresponding and alternate angles are equal.
Using the facts
A transversal crosses two parallel lines. One angle is $70^\circ$. Find the angle that is alternate to it, and the angle that is co-interior to it.
Two co-interior angles are $95^\circ$ and $87^\circ$. Are the lines parallel?
On parallel lines, one angle is $70^\circ$. Find its alternate angle.
Alternate angles are equal.
On parallel lines, one angle is $70^\circ$. Find its co-interior angle.
$180 - 70$.
Co-interior angles are $95^\circ$ and $87^\circ$. The lines are:
They add to $182^\circ$, not $180^\circ$.
Which pair makes a Z shape?
Z for alternate.
On parallel lines, an angle is $124^\circ$. Find its corresponding angle.
Corresponding angles are equal.
Co-interior angles on parallel lines are $3x^\circ$ and $60^\circ$. Find $x$.
$3x + 60 = 180$.
Alternate angles on parallel lines are $(4y + 5)^\circ$ and $65^\circ$. Find $y$.
$4y + 5 = 65$, so $4y = 60$.
Corresponding angles are $72^\circ$ and $72^\circ$. What can you conclude?
Equal corresponding angles prove lines are parallel.
New numbers every time. Keep going until you get five in a row.