Using Angles on the Same Arc Theorem

  • Context: MHB 
  • Thread starter Thread starter markosheehan
  • Start date Start date
  • Tags Tags
    Angles Arc Theorem
Click For Summary

Discussion Overview

The discussion revolves around the application of the angles on the same arc theorem in a geometric context. Participants are exploring how to utilize this theorem to analyze angles within a specific triangle configuration.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in applying the angles on the same arc theorem.
  • Another participant suggests drawing specific lines in the diagram to identify an external angle of triangle $BCD$.
  • A participant acknowledges seeing angles $CAL$ and $CBL$ after drawing the suggested lines.
  • It is noted that angle $CBL$ is identified as an external angle of triangle $BCD$, which relates to the theorem by being the sum of the two opposite angles.

Areas of Agreement / Disagreement

Participants appear to be working collaboratively to understand the theorem, with some initial confusion but ultimately reaching a point of clarity regarding the angles involved. No explicit consensus is stated.

Contextual Notes

There may be limitations in the clarity of the diagram or the specific relationships between the angles that are not fully resolved in the discussion.

Who May Find This Useful

Individuals interested in geometric theorems, particularly those involving angles and triangles, may find this discussion relevant.

markosheehan
Messages
133
Reaction score
0
View attachment 6471im trying to use angles on the same arc theorem
 

Attachments

  • WIN_20170313_12_36_15_Pro.jpg
    WIN_20170313_12_36_15_Pro.jpg
    59.8 KB · Views: 126
Mathematics news on Phys.org
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
 

Similar threads

MHB Formula to find arc radius using arc length, chord length, and/or segment angle
  • · Replies 4 ·
Replies
4
Views
6K
High School How to cut a plate onto a tube at an angle?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Find the Angle of Parable Tangent from Human Running Step
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the name of this geometry theorem?
  • · Replies 4 ·
Replies
4
Views
2K
High School Understanding the Pythagorean Theorem
  • · Replies 38 ·
2
Replies
38
Views
5K
High School Arc formula without the use of radius and angle
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Formal proof for the theorem of corresponding angles
  • · Replies 1 ·
Replies
1
Views
2K
Insights An Introduction to Theorema Primum
  • · Replies 0 ·
Replies
0
Views
3K
Prove that the field due to a circular arc is same as its bounded tangent at the centre of curvature
  • · Replies 23 ·
Replies
23
Views
1K
MHB How do I calculate the side of a rhombus using the bisector of an angle theorem?
  • · Replies 1 ·
Replies
1
Views
2K