Question

lesson 6
8 problems
practice problems
1 which of the following constructions would help to construct a line passing through point c that is perpendicular to the line ab in this diagram?
a construction of an equilateral triangle with one side ab
b construction of a hexagon with one side bc
c construction of a perpendicular bisector through c
d construction of a square with one side ab
2 two distinct lines l and m are each perpendicular to the same line n.
select all the true statements.
a lines l and m are perpendicular.
b lines l and n are perpendicular.
c lines m and n are perpendicular.
d lines l and m are parallel.
e lines l and n are parallel.
f lines m and n are parallel.

Explanation:

Step1: Analyze question 1

To construct a line through point C perpendicular to line AB, constructing a perpendicular bisector through C is relevant. Other constructions (equilateral - triangle, hexagon, square) don't directly help in constructing a perpendicular line from C to AB.

Step2: Analyze question 2

If two distinct lines l and m are each perpendicular to the same line n, then by the perpendicular - parallel relationship in a plane, lines l and n are perpendicular, lines m and n are perpendicular, and lines l and m are parallel.

Answer:

1. C
2. B, C, D