When a transversal cuts parallel lines corresponding angles are?

Two lines that are stretched into infinity and still never intersect are called coplanar lines and are said to be parallel lines. The symbol for "parallel to" is //.

If we have two lines (they don't have to be parallel) and have a third line that crosses them as in the figure below - the crossing line is called a transversal:

When a transversal cuts parallel lines corresponding angles are?

In the following figure:

When a transversal cuts parallel lines corresponding angles are?

If we draw to parallel lines and then draw a line transversal through them we will get eight different angles.

The eight angles will together form four pairs of corresponding angles. Angles F and B in the figure above constitutes one of the pairs. Corresponding angles are congruent if the two lines are parallel. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs.

Angles that are in the area between the parallel lines like angle H and C above are called interior angles whereas the angles that are on the outside of the two parallel lines like D and G are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles e.g. H and B.

Angles that share the same vertex and have a common ray, like angles G and F or C and B in the figure above are called adjacent angles. As in this case where the adjacent angles are formed by two lines intersecting we will get two pairs of adjacent angles (G + F and H + E) that are both supplementary.

Two angles that are opposite each other as D and B in the figure above are called vertical angles. Vertical angles are always congruent.

$$\angle A\; \angle F\; \angle G\; \angle D\;are\; exterior\; angles\\ \angle B\; \angle E\; \angle H\; \angle C\;are\; interior\; angles\\ \angle B\;and\; \angle E,\; \angle H\;and\; \angle C\;are\; consecutive\; interior\; angles\\ \angle A\;and\; \angle G,\; \angle F\;and\; \angle D\;are\; alternate\; exterior\; angles\\ \angle E\;and\; \angle C,\; \angle H\;and\; \angle B\;are\; alternate\;interior\; angles\\ \left.\begin{matrix} \angle A\;and\; \angle E,\; \angle C\;and\; \angle G\\ \angle D\;and\; \angle H,\; \angle F\;and\; \angle B\\ \end{matrix}\right\} \;are\; corresponding\; angles$$

Two lines are perpendicular if they intersect in a right angle. The axes of a coordinate plane is an example of two perpendicular lines.

In algebra 2 we have learnt how to find the slope of a line. Two parallel lines have always the same slope and two lines are perpendicular if the product of their slope is -1.

Video lesson

Find the value of x in the following figure

When a transversal cuts parallel lines corresponding angles are?

Corresponding angles are two angles that lie in similar relative positions on the same side of a transversal or at each intersection. They are usually formed when two parallel or non-parallel lines are cut by a transversal.

Remember that a transversal is a line that intersects two or more lines.

When a transversal cuts parallel lines corresponding angles are?

In our illustration above, parallel lines a and b are cut by a transversal which as a result, formed 4 corresponding angles. For example, \angle 2 and \angle 6 are corresponding angles. Why? Because both angles are located in matching corners or corresponding positions on the right-hand side of the transversal. In other words, each angle is located above the line and to the right of the transversal.

Here are our corresponding angles (must be in pairs) from the diagram and their location.

  • \angle \textbf{1} and \angle \textbf{5} – above the line, left of the transversal
  • \angle \textbf{3} and \angle \textbf{7} – below the line, left of the transversal
  • \angle \textbf{2} and \angle \textbf{6} – above the line, right of the transversal
  • \angle \textbf{4} and \angle \textbf{8} – below the line, right of the transversal

There are a few things to remember when dealing with corresponding angles.

Corresponding Angles Postulate

When two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent or have the same measure.

When a transversal cuts parallel lines corresponding angles are?

Take for example in our diagram above, since \angle 1 and \angle 5 are corresponding angles, they are congruent. This also means that if \angle 1 measures 70^\circ then \angle 5 also measures 70^\circ . Therefore, \angle 1 \cong \angle 5.

On the other hand, if the transversal intersects with two non-parallel lines, the corresponding angles formed are not congruent and do not have a specific relationship to each other.

When a transversal cuts parallel lines corresponding angles are?

Hence, \angle a and \angle e are corresponding angles but are NOT congruent.

Example 1: Identify the corresponding angles.

When a transversal cuts parallel lines corresponding angles are?

Here we have two parallel lines, lines k and g, that are cut by the transversal, t. Remember that corresponding angles are angles that are in similar positions on the same side of the transversal.

So the corresponding angles are:

  • \angle 2 and \angle 1
  • \angle 4 and \angle 3
  • \angle 6 and \angle 5
  • \angle 8 and \angle 7

Example 2: Name the pairs of corresponding angles and their location.

When a transversal cuts parallel lines corresponding angles are?

As you can see, the transversal cuts across two non-parallel lines forming 4 corresponding angles. Always remember that in this case, though the angles are located in corresponding positions relative to the two lines, they are not congruent.

The corresponding angles are:

  • \angle 3 and \angle 5 – above the line, left of the transversal
  • \angle 4 and \angle 6 – below the line, left of the transversal
  • \angle 2 and \angle 8 – above the line, right of the transversal
  • \angle 1 and \angle 7 – below the line, right of the transversal

Example 3: Find the measure of \angle 8.

When a transversal cuts parallel lines corresponding angles are?

Since line h and line w are parallel lines, the measure of \angle 8 should be the same as its corresponding angle. Hence, the m\angle 8 is 120^\circ.

You might also be interested in:

Alternate Exterior Angles

Alternate Interior Angles

Complementary Angles

Supplementary Angles

Vertical Angles