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

Given: DB bisects /ADC

AD congruent CD

Prove: DB ' AC

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- Dec 2nd 2013, 03:58 AMFentonjcDb 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.

Given: DB bisects /ADC

AD congruent CD

Prove: DB ' AC - Dec 2nd 2013, 04:26 AMMelody2Re: Db bisects adc help!!
- Dec 2nd 2013, 04:55 AMMelody2Re: Db bisects adc help!!
Hi Fentonjc,

I am going to assume that /ADC means angle ADC

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. - Dec 2nd 2013, 07:00 AMSorobanRe: Db bisects adc help!!
Hello, Fentonjc!

I am getting better at Mathematical Forensics.

II understand the problem . . .*think*

Quote:

$\displaystyle \text{Given: }\:\text{Triangle }ADC.$

. . . . . . $\displaystyle DB\text{ bisects }\angle ADC.$

. . . . . . $\displaystyle AD = CD$

$\displaystyle \text{Prove: }\:DB \perp AC$

Code:`D`

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A * - - - * - - - * C

B

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: .$\displaystyle DB \perp AC.$

- Dec 2nd 2013, 05:09 PMFentonjcRe: 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 - Dec 2nd 2013, 06:17 PMMelody2Re: 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!