Module 2: Lesson 6
 
Self-Check 3
  1. “Further Your Understanding” questions 2, 4, and 5, p. 72

    1. Equal angles include:

      • ∠EGB = ∠GHD are corresponding angles.
      • ∠EGA = ∠GHC are corresponding angles.
      • ∠AGH = ∠CHF are corresponding angles.
      • ∠BGH = ∠DHF are corresponding angles.
      • ∠EGB = ∠FHC are alternate exterior angles.
      • ∠EGA = ∠FHD are alternate exterior angles.
      • ∠BGH = ∠GHC are alternate interior angles.
      • ∠AGH = ∠DHG are alternate interior angles.

      There are other sets of angles that are not equal but are supplementary (i.e., add to 180°).

      • ∠BGH + ∠DHG = 180°(interior angles)
      • ∠AGH + ∠CHG = 180° (interior angles)
      • ∠AGE + ∠BGE = 180° (supplementary)
      • ∠AGH + ∠BGH = 180° (supplementary)
      • ∠CHG + ∠DHG = 180° (supplementary)
      • ∠CHF + ∠DHF = 180° (supplementary)
      • ∠EGA + ∠HGA = 180° (supplementary)
      • ∠EGB + ∠HGB = 180° (supplementary)
      • ∠DHF + ∠DHG = 180° (supplementary)
      • ∠CHF + ∠CHG = 180° (supplementary)

    1. The transversal is located on the top or bottom edge of the piece of wood. The T-bevel works by locking or holding the T edge at the same angle as the bevel is moved along the top edge of the wood, so you can draw lines that are at exactly the same angle.

      The T-bevel’s angle is adjusted by loosening the nut in the centre of the T and moving the top metal piece to the desired angle. This angle is locked into place by tightening the nut in the centre of the T so that the same angle can be drawn at different locations on the wood.

    2.  
      1. AB is not parallel to CD since the ∠EGB and ∠GHD are not equal.

      2. AB is parallel to CD since the alternate exterior angles of ∠EGB and ∠FHC are equal.

      3. ∠CHG = 86, °since it is supplementary to ∠CHF. Since ∠DHF and ∠EGB are interior alternate angles and are both 86°, AB is parallel to CD.

      4. AB is not parallel to CD. In the diagram, ∠BGH is 138° since it is opposite to the 138° angle marked. ∠CHF is supplementary to the 41° angle, so its measure is 180° − 41° = 139°. Since neither corresponding angles nor alternate interior angles are equal, the lines are not parallel. If they were parallel, ∠EGB would be 41°, as it is corresponding to 41. We would then have ∠ABE (138°) + ∠EGB (41°) = 180°, but they only add to 179°.