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# Triangle Geometry

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In triangle $ABC,$ $D$ is a point on $\overline{BC}$ such that $BD = DC = DA.$ If $\angle ABC = 45^\circ,$ then how many degrees are in $\angle ACB$?

Aug 5, 2023

### 8+0 Answers

#1
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I think the answer is 45 degrees, because angle abc is 45, and because BD = BC = BA, I think it is an isosceles. I'm not sure.

Aug 5, 2023
#4
+129742
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Good job, history !!!

CPhill  Aug 5, 2023
#2
+129742
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By SAS, triangle BDA  is similar to  triangle CDA

Angle ABD = Angle ACD  = Angle  ACB = 45

Aug 5, 2023
#3
+758
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Nice Job CPhiII. I was just guessing cuz I had no proof.

history  Aug 5, 2023
#5
+758
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Also, welcome back.  (Check the message I sent u xD)

history  Aug 5, 2023
#6
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Another way would be to note that ADB and ADC are congruent, which proves that the angle is 45 as well.

plaintainmountain  Aug 5, 2023
#7
+129742
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Thanks, plaintainmountain....I didn't think of that !!!

CPhill  Aug 5, 2023
#8
+758
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Nice thinking!

history  Aug 5, 2023