Math Proof: If an isosceles triangle has an altitude....

[mathilliterate]

:? I reached my last question for today and i still haven't been able to figure it out! Please if you can give me any advice or help!

If an isosceles triangle has an altitude from the vertex to the base, then the altitude bisects the vertex angle.
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CD bisects angle ACB

Statement Proof: Reasons
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[stapel]

How does point D relate the vertices A, B, and C? (I'm assuming that these latter points are the vertices of your isosceles triangle.)

Thank you.

Eliz.

 

[mathilliterate]

If i could draw it for you i would, picture a triangle. c is the point at the top, a is the left corner point b is the right corner point and a line is down the middle, which is d

 

[soroban]

Re: Math Proof Statements!! Please help and fast!!!!

Hello, mathilliterate!

If an isosceles triangle has an altititude from the vertex to the base,
then the altitude bisectc the vertex angle.

            C
            *
           /:\
          / : \
         /  :  \
        /   :   \
       /    :    \
      * - - + - - *
      A     D     B

Here's the game plan . . .

Show that \(\displaystyle \Delta CDA\) is congruent to \(\displaystyle \Delta CDB\).
\(\displaystyle \;\;\)We know that: \(\displaystyle \angle CDA\,=\,\angle CDB\,=\,90^o\;\) (CD is an altitude)
\(\displaystyle \;\;\)We know that: \(\displaystyle \angle A\,=\,\angle B\;\) (base angles of an isosceles triangle)
\(\displaystyle \;\;\)We know that: \(\displaystyle CA\,=\,CB\;\) (definition of an isosceles triangle)
That's enough to prove the two right triangles congruent.

Then \(\displaystyle \angle ACD\,=\,\angle BCD\;\)(corresponding parts of congruent triangles)
Therefore, \(\displaystyle CD\) bisects \(\displaystyle \angle C.\)

 

[mathilliterate]

Thank you so much! My night of homework is over!!!!!!!