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[Xayma]

But just to prove it:

Consider two parallel lines
y=m₁x+b
y=m₂x+c

Because they are parallel m₁=m₂

If a perpendicular line is drawn from each of the parallel lines so that they intersect, the slope of both lines would be m₃ where m₁=1/m₃ since m₁m₃=-1 for perpendicular lines.

ie the equation of the line from the first parallel line would be
y=m₃x+d
y=m₃x+e

As they intersect the angle between the lines can be found by using the formula tan @=|m_a-m_b/(1+m_am_b)|

Since the gradients are equal tan @=0 therefore @=180 degrees. Therefore they form a straight line ie they are the same line.

OR

A simpler way.

Since a line is perpendicular the angle between it and the line it is projected from is 90 degrees.

Corresponding angles between a transversal and two parallel lines = 180 degrees.

Therefore the other angle is 90 degrees therefore it is perpendicular to the other line, similarly the other line is perpendicular to both hence they are the same line and hence form a straight angle on interception.

 

[Grey Council]

for the clock question (now that my brain is working)

draw a clock
mark out every hour
join 12-6
join 12-7
join 7-0 (0 is centre of clock)
join 3-9
join 3-10
join 10-0
6-12-7 = 15 degrees
12-0-3 = 90 degrees
9-10-3 = 15 degrees
observe where lines 10-3 and 12-6 intersect. call that point X
0-X-3 = 75
so 0-X-10 = 105
so 12-X-10 = 75
so intersection of 12-7 and 10-3 meets at 90 degrees.

lol, just angle chased.

 

[Grey Council]

and there you go. Xayma actually did it properly.
and i used logic. stoopid examiners. I swear, they really should accept logic.

but nice proof Xayma.

 

[Giant Lobster]

lol omg..

didnt expect this question to last so long

 

[Grey Council]

its actually like 4 qusetions.