1. ## Db bisects adc help!!

Help I am totally lost. I have to do a proof problem with the statement and reason and I just don't get it.

Prove: DB ' AC

2. ## Re: Db bisects adc help!!

Originally Posted by Fentonjc
Help I am totally lost. I have to do a proof problem with the statement and reason and I just don't get it.

Prove: DB ' AC
I am going to demonstrate my lack of knowledge immediately by asking you to explain what the symbols mean. Please.
That is /ADC what is the forward slash
and
what is the apostrophy.

3. ## Re: Db bisects adc help!!

Originally Posted by Fentonjc

Prove: DB ' AC
Hi Fentonjc,

and DB ' AC means DB bisects AC (the only other alternative that I can think of is that DB is perpendicular to AC and the proof would be similar)

Draw the picture first of course
Let X be the intersection of DB and AC

Consider triangle ADX and triangle CDX

you can prove that these 2 triangles are congruent and hence show that AX=CX
then give a concluding statement and you are finished.

Is that enough help?
Melody.

4. ## Re: Db bisects adc help!!

Hello, Fentonjc!

I am getting better at Mathematical Forensics.
I think I understand the problem . . .

$\displaystyle \text{Given: }\:\text{Triangle }ADC.$
. . . . . . $\displaystyle DB\text{ bisects }\angle ADC.$
. . . . . . $\displaystyle AD = CD$
$\displaystyle \text{Prove: }\:DB \perp AC$

Code:
              D
*
/|\
/ | \
/  |  \
/   |   \
/    |    \
/     |     \
/      |      \
A * - - - * - - - * C
B
We are given: .$\displaystyle AD = CD.$

We are told that $\displaystyle DB$ bisects $\displaystyle \angle ADC.$
Then: .$\displaystyle \angle BDA = \angle BDC$

Also: .$\displaystyle DB =DB$ (Identity)

So: .$\displaystyle \Delta DBA \cong \Delta DBC$ (s.a.s.)

Hence: .$\displaystyle \angle DBA = \angle DBC$ (corresponding parts)

We see: .$\displaystyle \angle DBA + \angle DBC \,=\,180^o$

Since $\displaystyle \angle DBA = \angle DBC,\;\angle DBA = 90^o$

Therefore: .$\displaystyle DB \perp AC.$

5. ## Re: Db bisects adc help!!

I tried to attach the actual picture. Then it has a box that has 2 sides ones says statements and the other says reasons.

it is a triangle that has a D on top and A B C on the bottom and it also has a 1 and 2 inside the triangle under the D

6. ## Re: Db bisects adc help!!

There you go Soroban. You are good at Forensic mathematics! You even had the diagram around the right way.
I'm impressed.

I have a soroban. It was given to me by a Japanese exchange student. It was a great gift!