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[J2 Cool]

Been helping out my brother with this college-prep geometry packet. Actually his last packet in this home schooling he's done to get his scholarship while he's had to work this past year or so. But anyway, Im just looking for help on 2 problems real quick if you can.

First,

Given : In Triangle ABC, angle B = 120 degrees
Prove: Angle A =(with a slash like "/" through it) 60 degrees
Plan: Use an indirect proof

NOTE: Write the proof using the paragraph method.





And Second.

Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a two-column proof.
HINT: It will help if you draw a diagram with the points labeled.

Given:
Prove:
Plan:


Oh, and much much thanks in advance to whoever helps. Out of about 10 exams each containing 30-50 problems these were some painstaking to be stuck on and eventually skip.

 

[Mr Gump]

For the first one, the angle sum of a triangle is 180 so if B = 120 its impossible for A to = 60.

 

[Ferrio]

The 2nd one, well been a long time in geometry I can't give an official sounding proof but here's the run down.



A line tangent to the endpoint of the diameter makes a 90 degree angle. The other tangent line on the opposite endpoint of the diameter makes a 90 degree angle. They're both perpendicular to the same line, so t hey must be parallel

 

[TheQueen'sOwn]

Just create a circle, label it, and come up with appropriate equations for the tangents of the endpoints of the circle's diameter.

Use substitution or elimination to come up with one equation.
Factor if you must.
and you will determine that there is 0 P.O.I. and that they are therefore parallel.

 

[Dilbert]

The answer for the first one is already posted, but I'm not sure that Mr Gump used an indirect proof method. You could prove that angle A can't be 60 degrees with a reductio ad absurdam ("reduction to the absurd," sometimes called "proof by contradiction") argument like this one:

Postulate 1: The sum of the angles in any triangle is 180 degrees. Postulate 2: Each angle in a triangle must be greater than 0 degrees. Label the angles in this particular triangle A, B, and C, with B equal to 120 degrees. Let us suppose that angle A was equal to 60 degrees. If that were the case, then angle C would be 0 degrees by our first postulate. However, this contradicts the second postulate! Therefore, our supposition is wrong, and angle A cannot be 60 degrees.

As for the second one, I don't remember formal geometry proof steps off the top of my head. One approach that you might take is this, though:

-> A diameter, by definition, is a single line segment connecting two points on the edge of a circle and containing the center of a circle.
-> A tangent, by definition, is a line which touches the circle in exactly one point.
-> A tangent line is perpendicular to the radius which starts at the center of the circle and ends at the point of tangency. (You can show separately that each tangent line on either side of the diameter is perpendicular to the diameter.)
-> Perpendicular lines, by definition, contain right angles.
-> The alternate interior angles (you might want to check that term) formed by the two tangent lines and the diameter are supplementary (add to 180 degrees).
-> When two lines are crossed by a transversal (the diameter, in this case) and the alternate interior angles are supplementary, then the lines are parallel.

The last step is certainly true, but I'm not sure that your book will have that as a proved theorem already. Usually, you start with the postulate that you have two parallel lines cut by a transversal, and then you prove that the alternate interior angles are supplementary. Here, we are going backwards.

Hope this helps...

 

[J2 Cool]

thanks a lot to all you guys. This definetly helped a lot

 

[levious]

SOH CAH TOA