Need help, 3 problems to graduation!!! please help!!

**proofsRkickingmybutt** · Feb 3rd 2009, 03:11 PM

Hi All, I'm a student of The American school and the only thing I have between me and my diploma is 3 proofs. I've gotten help from several people but we can't seem to figure out these proofs. Any help would be awesome!!

Given: In triangle ABC, (angle) B = 120 degrees

Prove: Angle A is not equal to 60 degrees

Plan: Use an indirect proof.

NOTE: Write the proof using the paragraph method.

Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. (State your plan and give a proof.)

Given: ABCD is a parallelogram with (angle) 1 congruent with (angle) 2

To Prove: ABCD is a rhombus

Plan:

Thanks to Soroban for help with this proof =)

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.

Thanks so much to anyone who can help me with one or all of these proofs. I'm so ready to be finished with High School LOL

**Soroban** · Feb 3rd 2009, 05:05 PM

Hello, proofsRkickingmybutt!

Here's the second one . . .

Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram,
the parallelogram is a rhombus.

Given: $ABCD$ is a parallelogram with $\angle1 = \angle2$

To Prove: $ABCD$ is a rhombus.

We need to prove that two adjacent sides are equal.

Code:

          A * - - - - - - - - * B
           /2 * 1            /
          /     *           /
         /        *        /
        /           *     /
       /            3 * 4/
    D * - - - - - - - - * C

$1.\;\angle1 = \angle 2$ . . . . . . . . . . $\text{Given}$

$2.\;AB \parallel DC,\:AD \parallel BC$ . . $\text{d{e}f. parallelogram}$

$3.\;\angle1 = \angle 3,\:\angle 2 = \angle 4$ . . . $\text{alt-int. angles}$

$4.\;\angle1 \,=\,\angle 4$ . . . . . . . . . $\text{Transitivity}$

$5.\;\Delta ABC\text{ is isosceles}$ . . . $\text{d{e}f. isosceles}$

$6.\;\therefore\:AB = BC$ . . . . . . $\text{d{e}f. isosceles}$

. . . $Q.E.D.$

**proofsRkickingmybutt** · Feb 3rd 2009, 05:52 PM

Oh Thank you SOOOOO much!!!

=D!!

**Soroban** · Feb 3rd 2009, 07:17 PM

Hello, proofsRkickingmybutt!

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.

Code:

                A
    P - - - - * * * - - - - Q
          *     |     *
        *       |       *
       *        |        *
                |
      *         |         *
      *         *O        *
      *         |         *
                |
       *        |        *
        *       |       *
          *     |     *
    R - - - - * * * - - - - S
                B

There is a Theorem that says:
. . If a line is tangent to a circle, the radius drawn to
. . the point of tangency is perpendicular to the tangent.

We have a circle with center $O$ and diameter $AB.$

Line $PQ$ is tangent to circle $O$ at $A.$
Line $RS$ is tangent to circle $O$ at $B.$

$1.\;OA \perp PQ,\:OB \perp RS$ . . . . . $\text{Theorem}$

$2.\;\angle OAP = 90^o,\:\angle OBS = 90^o$ . . $\text{d{e}f. perpendicular}$

$3.\;\angle OAP = \angle OBS$ . . . . . . . . . $\text{All right angles are equal.}$

$4.\;\therefore\:PQ \parallel RS$ . . . . . . . . . . . $\text{alt-int. angles}$

**Unenlightened** · Feb 3rd 2009, 07:37 PM

Originally Posted by proofsRkickingmybutt

Given: In triangle ABC, (angle) B = 120 degrees

Prove: Angle A is not equal to 60 degrees

Plan: Use an indirect proof.

NOTE: Write the proof using the paragraph method.

I'm guessing it's too trivial to say that if B is 120 degrees, and A is 60 degrees, then C must be equal to 180 (total number of degrees in a triangle) - 180 = 0... which is clearly nonsense... and therefore A is less than or at least, not equal to 60?

Edit: Unless you're supposed to prove the sum of the angles in a triangle = 180 degrees... but that's been done to death

Thread: Need help, 3 problems to graduation!!! please help!!

LinkBack

Thread Tools

Display

Need help, 3 problems to graduation!!! please help!!

Similar Math Help Forum Discussions

memory problems/concentration problems with age?

binomial problems/normal problems

binomial problems as normal problems

Problems with integration word problems

Jordan Curve (high level, graduation level)

Search Tags