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Given two parallel lines and a transversal we know that corresponding angles are congruent, alternate interior angles are congruent, and same-side interior angles are congruent.
4) (a) w=120 as it is a vertical angle,y=60 as it is supplementary to 120, and x=60 as it is corresponding to y
(b) a=112 (corresponding),b=55 (vertical to f), c=68 (supplementary),d=55 (vertical),e=112 (vertical to a), and f=55 (alternate interior to d)
8) (a) perpendicularity does not possess the transitive property. (Equality, congruence, and inequality all have the transitive property.) Note that, if the lines were in a plane, the lines would be parallel. In space, the lines could be skew, parallel, or perpendicular.
(b) In a plane, 2 lines perpendicular to the same line are parallel.
10) Replace the reason for line two -- QP parallel to RS since they form supplementary angles (both 90 degrees) that are in the interior of two lines cut by a transversal.
12) RS parallel to OX since two lines are cut by a transversal such that corresponding angles are congruent.
QP parallel to OX for the same reason.
So for number 3.
All that you need to remember is that parallel lines cut by a transversal will create congruent angles. There are three types of angles that are congruent in this case.
The first one is alternate interior angles. This is when the angles are between the parallel lines. So in your question angle k does equal angle p because they both lie inside the vertical parallel lines.
The second way is through alternate exterior angles. That is when the angles are on opposite ends of the transversal and are outside the two parallel lines. So angle j and q are equal because of alternate exterior angles because they lie outside the two vertical parallel lines.
The third way is through corresponding angles where the angles are in matching corners. So angle a and angle j are corresponding angles becaus they both are in the top left corner.
There is one more way to get congruent angles and that is by vertical angles. These are angles that share the same vertex. Unlike the other ways mentioned above this one involved only one vertex. So angle g and angle d are considered vertical angles because are in the same vertex and they are directly across from each other.
For the question h) it is correct because interior angles add up to 180 degrees.
What about three and 15 ?
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