3.3. Corresponding Angles http://www.ck12.org
Guidance
Corresponding Anglesare two angles that are in the “same place” with respect to the transversal, but on different
lines. Imagine sliding the four angles formed with lineldown to linem. The angles which match up are correspond-
ing.
Corresponding Angles Postulate:If twoparallel lines are cut by a transversal, then the corresponding angles are
congruent.
Ifl||mand both are cut byt, then^61 ∼=^65 ,^62 ∼=^66 ,^63 ∼=^6 7, and^64 ∼=^6 8.
Converse of Corresponding Angles Postulate:If corresponding angles are congruent when two lines are cut by a
transversal, then the lines are parallel.
Investigation: Corresponding Angles Exploration
You will need: paper, ruler, protractor
- Place your ruler on the paper. On either side of the ruler, draw lines, 3 inches long. This is the easiest way to
ensure that the lines are parallel. - Remove the ruler and draw a transversal. Label the eight angles as shown.
- Using your protractor, measure all of the angles. What do you notice?
In this investigation, you should see thatm^61 =m^64 =m^65 =m^6 8 andm^62 =m^63 =m^66 =m^6 7.^61 ∼=^64 ,^65 ∼=
(^6) 8 by the Vertical Angles Theorem. By the Corresponding Angles Postulate, we can say 6 1 ∼= (^6) 5 and therefore
6 1 ∼= (^6) 8 by the Transitive Property.
Investigation: Creating Parallel Lines using Corresponding Angles
- Draw two intersecting lines. Make sure they are not perpendicular. Label themlandm, and the point of
intersection,A, as shown. - Create a point,B, on linem, aboveA.
- Copy the acute angle atA(the angle to the right ofm) at pointB. See Investigation 2-2 in Chapter 2 for the
directions on how to copy an angle. - Draw the line from the arc intersections to pointB.
From this construction, we can see that the lines are parallel.
Example A
Ifm^68 = 110 ◦andm^64 = 110 ◦, then what do we know about lineslandm?
(^6) 8 and (^6) 4 are corresponding angles. Sincem (^68) =m (^6) 4, we can conclude thatl||m.
Example B
Ifm^62 = 76 ◦, what ism^6 6?
(^6) 2 and (^6) 6 are corresponding angles andl||m, from the markings in the picture. By the Corresponding Angles
Postulate the two angles are equal, som^66 = 76 ◦.