Using Angles on the Same Arc Theorem

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SUMMARY

The discussion centers on the application of the Angles on the Same Arc Theorem in geometry. Participants emphasize the importance of drawing lines AL and BC to identify external angles in triangle BCD. Specifically, angle CBL is highlighted as an external angle that equals the sum of the two opposite angles, angle CAL and angle CBL. This theorem is crucial for solving problems involving cyclic quadrilaterals and triangle properties.

PREREQUISITES
  • Understanding of the Angles on the Same Arc Theorem
  • Basic knowledge of triangle properties and external angles
  • Familiarity with cyclic quadrilaterals
  • Ability to interpret geometric diagrams
NEXT STEPS
  • Study the properties of cyclic quadrilaterals in depth
  • Learn about external angles in triangles and their applications
  • Explore advanced geometric theorems related to circles
  • Practice solving problems involving the Angles on the Same Arc Theorem
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Students studying geometry, educators teaching geometric theorems, and anyone looking to enhance their understanding of circle-related properties in mathematics.

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View attachment 6471im trying to use angles on the same arc theorem
 

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markosheehan said:
im trying to use angles on the same arc theorem
Yes, the same arc theorem will certainly come into it. I suggest that you draw the lines $AL$ and $BC$ in the diagram, and then look for an external angle of the triangle $BCD$.
 
sadly i still can't see it... I've drawn these lines. all i can see now is angleCAL and angleCBL
 
markosheehan said:
sadly i still can't see it... I've drawn these lines. all i can see now is angleCAL and angleCBL
That's right! Angle $CBL$ is an external angle of the triangle $BCD$, so it is the sum of the two opposite angles.
 
see it now
 

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