http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
- 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.