Due 11/30, Prep for 3.4
Nov 28th, 2011 by corricelli
Hello,
HW Due on 11/30: Read and take notes on pages 150-152.
Do p. 153: 1-9.
Feel free to post questions/concerns/teamwork.
You can reply to a teammate’s question by pressing the green reply button and typing your response.
Happy homeworking,
Mrs. Corricelli
I was checking my answers with the back of the book and for #5 the question is “Can you prove that lines p and q are parallel? If so, describe how.” and the 2 lines and the transversal form 4 right angles. I said that yes they are parallel because of the Perpendicular Transversal Theorem. I don’t understand how I’m wrong?
Parker,
In number 5 the two lines do not form right angles. I am not sure what you mean. Right angles are marked with boxes, like little squares. These markings are arcs, indicating that they are congruent, not necessarily that they are right angles. I hope I am looking at the right problem? At any rate, the pair of angles that was marked to be congruent do not meet any of the special pairs mentioned. They are not alternate interior angles, alternate exterior angles, or corresponding angles, so we cannot conclude (by any converse) that the lines are parallel. See my response to Libby also on this page for more information.
Happy homeworking,
Mrs. Corricelli
I am confused on numbers 3-8 on the hw. It asks if lines p and q are parallel…but wouldn’t they all be parallel since p and q never intersect and are coplanar?
Libby,
So NOW we are looking at converses to the theorems (and the one postulate, corresponding angles postulate) we have come to know and love in 3.1-3.3.
So thinking about converses… let’s look at the corresponding angles postulate. That postulate says “If two lines are parallel then the corresponding angles formed by those two lines cutting through a transversal are congruent.” SO, its converse, called the “corresponding angles postulate converse” would be, “If two corresponding angles formed by two lines cutting through a transversal are congruent, THEN the lines are parallel.” Do the same thing for the other theorems, namely the alternate interior angles theorem, the alternate exterior angles theorem, and the consecutive interior angles theorem and you have four tests (including the corresponding angles postulate converse) to decide if lines are parallel. If these special pairs of angles are not among the ones listed then you cannot say that the lines are parallel.
For example, number 3. See how the alternate exterior angles are marked congruent? By the alternate interior angles theorem converse, then, we can now conclude that the lines that formed them (p and q) are parallel. See how in number 4 you cannot make the same leap. A pair of vertical angles does not at all guarantee parallelity. Parallel lines are not at all part of the vertical angles theorem, plus the converse is not discussed to be true. In class tomorrow and for hw tomorrow, you will be proving the truth of these theorems!
Happy homeworking,
Mrs. Corricelli
Mrs.Corricelli, would we be doing this in the S and R chart?
Matt S,
Yes!