anonymous
  • anonymous
D is the midpoint of AC, BDC=BDA prove ABD=CBD
Mathematics
jamiebookeater
  • jamiebookeater
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ash2326
  • ash2326
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ash2326
  • ash2326
In triangle ABD and CDB AD=DC (Since D is the midpoint) BD= BD (common side) and angle BDA= angle BDC so by SAS (side angle side) the two triangles are congruent using CPCTC angle ABD= angle CBD
anonymous
  • anonymous
By inspection, line AC has to be normal to line BD in order for the angles in question to be equal.\[\text{ABD}=\text{ArcTan }\left[\frac{\text{AD}}{\text{BD}}\right],\text{DBC}=\text{ArcTan }\left[\frac{\text{DC}}{\text{BD}}\right] \]AD=DC, so the angles ABD and DBC are equal to each other.

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