I'm not sure how to complete this

[Wormman12]

Sorry if this is in the wrong place. idk if its algebra, and all my class says is college math II. this isn't anything needing to be graded, but an exorcise I did on the spare to try to figure out.


So for this, I identified that because line CD is perpendicular to line AB, it creates two supplementary right angles at CDA and CDB. I also identify that line AD=AB-DB and that line DB=AB-AD so those two sides can be considered similar. from this, I need to either prove that another side is similar, or that another angle is congruent. I wanna prove that angles ACD and DCB are congruent, but I am not sure if altitudes bisect the angle. anyone know how to help, that would be real nice. I have a quiz tomorrow, and though I doubt it will be on the test, I would love to be prepared.

 

[Deleted member 4993]

Sorry if this is in the wrong place. idk if its algebra, and all my class says is college math II. this isn't anything needing to be graded, but an exorcise I did on the spare to try to figure out.
View attachment 2597

So for this, I identified that because line CD is perpendicular to line AB, it creates two supplementary right angles at CDA and CDB. I also identify that line AD=AB-DB and that line DB=AB-AD so those two sides can be considered similar. from this, I need to either prove that another side is similar, or that another angle is congruent. I wanna prove that angles ACD and DCB are congruent, but I am not sure if altitudes bisect the angle. anyone know how to help, that would be real nice. I have a quiz tomorrow, and though I doubt it will be on the test, I would love to be prepared.

You need to show that the triangle ACD is similar to triangle ACB

and

You need to show that the triangle DCB is similar to triangle ACB

Then you can it is proven that triangle ACD is similar to triangle DCB

In these two triangles,

angle ADC = Angle CDB = 90°

angle ACD = angle CBD

and

angle DAC = angle DCB

 

[Wormman12]

You need to show that the triangle ACD is similar to triangle ACB

and

You need to show that the triangle DCB is similar to triangle ACB

Then you can it is proven that triangle ACD is similar to triangle DCB

In these two triangles,

angle ADC = Angle CDB = 90°

angle ACD = angle CBD

and

angle DAC = angle DCB[/QUOTE]

Okay, I think I get what your saying, but how do I prove that angle ACD is similar to ACB? If you can simplify in a few steps that would be great.

 

[Wormman12]

Do you know what "similar triangles" means?
Did you google "similar triangles"?

Yes. I know what similar triangles are. the problem is, I don't know the steps I should take to prove it. I don't know how to prove that either triangles ACD or CDB are similar to triangle ABC.

 

[Deleted member 4993]

Yes. I know what similar triangles are. the problem is, I don't know the steps I should take to prove it. I don't know how to prove that either triangles ACD or CDB are similar to triangle ABC.

Please tell us the criterion of "similar" triangles.