In a plane, prove that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. (Theorem 3.4)

Use the following statement and the definitions and postulates you know to answer each question. Two planes are perpendicular if and only if one plane contains a line perpendicular to the second plane. a. Through a given point, there passes one and only one plane perpendicular to a given line. If plane Q is perpendicular to line l at point X and line l lies in plane P, what must also be true? b. Through a given point, there passes one and only one line perpendicular to a given plane. If plane Q is perpendicular to plane P at point X and line a lies in plane Q, what must also be true?

Indicate whether each statement is True (T) or False (F). a. If a plane contains one of two skew lines, it contains the other. b. If a line and a plane never meet, they are parallel. c. If two parallel lines lie in different planes, the planes are parallel. d. If a line is perpendicular to two planes, the planes are parallel. e. If a plane and a line not in the plane are each perpendicular to the same line, then they are parallel to each other.

Indicate whether each statement is True or False. Be prepared to defend your choice. a. Two lines must either intersect or be parallel. b. In a plane, two lines perpendicular to the same line are parallel. c. In space, two lines perpendicular to the same line are parallel. d. If a line is perpendicular to a plane, it is perpendicular to every line in the plane. e. It is possible for two planes to intersect at one point. f. If a line is perpendicular to a line in a plane, it is perpendicular to the plane. g. Two lines perpendicular to the same line are parallel. h. A triangle is a plane figure. i. A line that is perpendicular to a horizontal line is vertical. j. Three parallel lines must be coplanar. k. Every four-sided figure is a plane figure.

A farmer raises chickens and pigs. If his animals have a total of 120 heads and a total of 300 feet, how many chickens does the farmer have? F 60 G 70 H 80 J 90