Friday, October 10

NOTE:  I extend my sincerest apologies for my delay in posting the HW assignment to this blog.  A technical glitz followed by a trip out of town have resulted in my not updating this blog until Sunday evening.  Due to the decrease in time available, I have cut back on the initial assignment.  Thank you for your understanding.

Geometry - In Sec. 3.3, we turned things around and explored the converse of the properties of parallel lines that we discussed in Sec. 3.2.  These newly proven theorems provide us with a way to prove that two lines are parallel.

Homework for THURSDAY - Complete the remainder of the Sec. 3.2 proof worksheet that we discussed at the beginning of class on Friday.  In addition, complete the following problems in your text:  pgs. 166 - 167  #4-10, #22, #24-35.  Finally, complete this worksheet highlighting proving lines parallel.

Property of Parallel Lines (Sec. 3.2)

If two lines are parallel, then they are coplanar and do not intersect.  We went on to explain that these must also "run in the same direction" and mus "always lie an equal distance apart".  Definition of Parallel Lines)

- If two lines cut by a transversal are parallel, then each pair of corresponding angles must be congruent.  (Corresponding Angle POSTULATE - If || --> corr < congruent)

- If two lines cut by a transversal are parallel, then each pair of alternate interior angles must be congruent.  (Alternate Interior Angle THEOREM - If || --> alt int < congruent)

- If two lines cut by a transversal are parallel, then each pair of alternate exterior angles must be congruent.  (Alternate Exterior Angle THEOREM - If || --> alt ext < congruent)

- If two lines cut by a transversal are parallel, then each pair of same side interior angles must be supplementary.  (Same Side Interior Angle THEOREM - If || --> s s int < supp)

- If two lines cut by a transversal are parallel, then each pair of same side exterior angles must be supplementary.  (Same Side Exterior Angle THEOREM - If || --> s s ext < supp)

Ways to Prove Two Lines are Parallel (Sec. 3.3)

- If a pair of corresponding angles are congruent, then the coplanar lines (cut by a transversal) that form them must be parallel. (CONVERSE of Corresponding Angle Postulate POSTULATE - If corr < congruent, then ||)

- If a pair of corresponding angles are congruent, then the coplanar lines (cut by a transversal) that form them must be parallel. (If alt int < congruent --> ||)

- If a pair of corresponding angles are congruent, then the coplanar lines (cut by a transversal) that form them must be parallel. (If alt ext < --> ||)

- If a pair of corresponding angles are congruent, then the coplanar lines (cut by a transversal) that form them must be parallel. (If s s int < supp --> ||)

- If a pair of corresponding angles are congruent, then the coplanar lines (cut by a transversal) that form them must be parallel. (If s s ext < supp --> ||)

- If two lines are parallel to the same line, then they are parallel to each other.  (If || to same line --> ||)

- If two lines are perpendicular to the same line, they they are parallel to each other. (If  |  to same line --> ||)