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In the figure, lines l and m are parallel. Which one of the following, if true, makes lines p and q parallel?
(A) a = b
(B) a = c
(C) c = d
(D) d = b
(E) b = c
Attachments
lines (1).jpg [ 17.37 KiB | Viewed 5213 times ]
09 Oct 2018, 07:44
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Bunuel
In the figure, lines l and m are parallel. Which one of the following, if true, makes lines p and q parallel?
(A) a = b
(B) a = c
(C) c = d
(D) d = b
(E) b = c
Attachment:
lines (1).jpg
If p and q are parallel, so the quadrilateral formed by these lines is parallelogram..
Opposite angles of a parallelogram are equal, so b=c
E
12 Oct 2018, 07:54
Kudos
Bookmarks
Bunuel
In the figure, lines l and m are parallel. Which one of the following, if true, makes lines p and q parallel?
(A) a = b
(B) a = c
(C) c = d
(D) d = b
(E) b = c
Attachment:
lines (1).jpg
Since lines l and m are parallel, the quadrilateral is either a trapezoid (only lines l and m are parallel) or a parallelogram (if lines p and q are also parallel).
We see that the angles with measures of b and c degrees are opposite angles of the quadrilateral. If they are equal, i.e., if b = c, then the quadrilateral is a parallelogram (it won’t be a trapezoid since opposite angles of a trapezoid are not equal in measure). So if b = c, we have a parallelogram, which means that lines p and q are parallel.
Answer: E
