Corresponding Angles
In short: Corresponding angles occupy the same corner at two different intersections along a cutting line, and for parallel lines each such pair has identical measures.
8th GradeGeometry8.G.A.5
What is Corresponding Angles?
Slide the first intersection down along the cutting line until it lands on the second, and angles that fall in the same corner, say both upper left, are corresponding angles; each of the four corners supplies one pair.
If the two cut lines are parallel, every pair of this kind is congruent. Showing a single equal pair also proves that the lines are parallel.
How to spot it
- Two angles occupy the same corner position, such as both upper right, at two different intersections.
- The diagram shows an F shape formed by the transversal and the two lines.
- Two roads or beams are declared parallel and the question wants every pair of equal angles named.
- One angle is given at the upper crossing, and you must find the same-corner angle at the lower one.
The method
- Name the crossing you know and the crossing you want, then pick one corner, like lower right.
- Find the angle in the identical corner at the other crossing; that is the corresponding angle.
- If the lines are parallel, copy the measure straight across.
- For a different corner, use a straight angle (sum \(180^{\circ}\)) or vertical angles to move around the crossing.
Corresponding Angles: solved example
Problem
Two parallel rafters in a barn are crossed by a diagonal brace. At the top rafter the angle above the rafter and to the right of the brace is \((5x + 8)^{\circ}\). At the lower rafter the angle in the same corner is \(118^{\circ}\). Find x.
Solution
These are corresponding angles on parallel rafters, so \(5x + 8 = 118\).
Subtract 8: \(5x = 110\). Divide by 5: \(x = 22\). Check: \(5(22) + 8 = 118\).
Try it
Question 1
Parallel lines are cut by a transversal. The lower-left angle at the first crossing is \(49^{\circ}\). What is the lower-left angle at the second crossing?
Show the answer
It is also \(49^{\circ}\), since the corners match and the lines are parallel.
Question 2
The upper-right angle at one crossing is \(75^{\circ}\). Find the upper-left angle at the other crossing if the lines are parallel.
Show the answer
The upper-right angle there is \(75^{\circ}\); the upper-left is its straight-line neighbor: \(180^{\circ} – 75^{\circ} = 105^{\circ}\).
Corresponding Angles vs. Vertical Angles
Vertical angles share one crossing and face each other across it; they are equal every time. Corresponding angles belong to two different crossings and sit in matching corners; they are equal only for parallel lines. Count the crossings to tell them apart.
Keep going
Lessons
Worksheets and quizzes
- Angles in Triangles and Parallel Lines – Worksheet
- Angles in Triangles and Parallel Lines – Quiz
- Parallel Lines and Transversals – Worksheet
- Parallel Lines and Transversals – Quiz
Related words
Whole dictionary: A–Z · 8th Grade · Geometry