Question

Complete the following proof.

Answer 1

heres the question

Answer 2

Hmm this is pretty obvious, i think they require a better explanation thats all. So here goes.

GIve that the RS line is a straight line. Assuming it has a gradient of x.
Since AR and BS are tangential to this line, meaning it is perpendicular to this line, RS.
AR and BS both will have gradient of -1/x.

Since AR and BS have the same gradient, they must be parallel.

Answer 3

i think if u join the line A-B N THEN DRAW ANOTHER LINE FROM A PERPENDICULAR TO THE LINE BS N GIVE IT A NAME SAY AS E, THEN U WILL GET A RECTANGLE ARSE, THEN IN A RECTANGLE OPPOSITE SIDES ARE EQUAL N PARALLEL AS U KNOW.

Answer 4

OK thanks both of you too hard to give best answer.

Answer 5

AH........... OK.....

Answer 6

sorry Tiaph

Answer 7

There are a number of ways to prove this. I like Tiaph's way. I also like this approach:
Circle A is tangent to line RS, so the radius AR is perpendicular to RS.
AR is perpendicular to RS, so angle ARS = 90 degrees.
Circle B is tangent to line RS, so the radius BS is perpendicular to RS.
BS is perpendicular to RS, so angle BSR = 90 degree.
Lines AR and BS are cut by the transversal RS, and the same side interior angles ARS and BSR sum to 180. Therefore, the lines AR and BS are parallel.

Answer 8

By the way, that is appealing to Euclid's fifth postulate, the parallelism postulate.

Answer 9

@sradha, line AB may not be parallel to line RS. The others have it right.

Answer 10

Yeah, Sradha's suggestion is actually incorrect unless the circles are the same size.

Answer 11

NO ITS NOT PARALLEL BUT BY JOINING THE LINE AB N DRAWING ANOTHER LINE FROM A PERPENDICULAR TO THE LINE BS N MARK THAT POINT AS E WE GE A TRIANGLE AS ABE. N THE LOWER PORTION i.e ARSE IS A RECTANGLE NOW AND EACH ANGLE WE GET 90 DEGREE.... N IN A RECTANGLE OPPOSITE SIDES ARE EQUAL N PARALLEL.

Answer 12

Can you please stop with the caps.

Answer 13

Seriously, and what is your justification for claiming that it is a rectangle?

Answer 14

You can do that proof, but you do need to give a justification for saying that all of the angles are right angles.

Answer 15

ITS THE DRAWING