Chapter 6: Q5. (page 212)
Complete the following statement with the word always, sometimes, or never.
Two lines parallel to a third line are _____ parallel.
The complete statement is “Two lines parallel to a third line are always parallel”.
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Suppose someone plans to write an indirect proof of each conditional. Write a correct first sentence of the indirect proof.
If , then
For the following figure, find the measures of and .
Write the letters (a)-(d) in an order that completes an indirect proof of the statement: Through a point outside a line, there is at most one line perpendicular to the given line.
Given: Point P not on the line k.
Prove: There is at most one line through P perpendicular to k.
(a) But this contradicts corollary3 of theorem 3-11: In a triangle, there can be at most one right angle or obtuse angle.
(b) Then and are right angles, and has two right angles.
(c) Thus, our temporary assumption is false, and there is at most one line through P perpendicular to k.
(d) Assume temporarily that there are two lines through P perpendicular to k at A, B.
Write the reasons that justify the statements.
Given: contain point Z. Prove:
Complete the proof if given is and .
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