Geometry: proving two angles are equal

  • Context: MHB 
  • Thread starter Thread starter markosheehan
  • Start date Start date
  • Tags Tags
    Angles Geometry
Click For Summary
SUMMARY

The discussion focuses on proving the equality of two angles using the properties of a circle with diameter $OC$. It emphasizes that any angle inscribed in a semicircle is a right angle, which directly leads to the conclusion that the angles in question are equal. The geometric principles involved include the inscribed angle theorem and the properties of diameters in circles.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly circles and angles.
  • Familiarity with the inscribed angle theorem.
  • Knowledge of how diameters relate to angles in a circle.
  • Ability to visualize geometric figures and their properties.
NEXT STEPS
  • Study the inscribed angle theorem in detail.
  • Explore the properties of circles, focusing on diameters and their implications for angles.
  • Practice problems involving angle proofs in circles.
  • Learn about other geometric theorems related to angles and circles.
USEFUL FOR

Students studying geometry, educators teaching geometric principles, and anyone interested in mastering angle proofs in circular geometry.

markosheehan
Messages
133
Reaction score
0
View attachment 5962

can some one show me how to work this out
 

Attachments

  • WIN_20160908_20_51_25_Pro.jpg
    WIN_20160908_20_51_25_Pro.jpg
    52.4 KB · Views: 115
Mathematics news on Phys.org
Re: geomertry

Hint: What can you say about the circle that has $OC$ as a diameter?
 

Similar threads

Undergrad What is the name of this geometry theorem?
  • · Replies 4 ·
Replies
4
Views
2K
High School Reprise: Calculate the distance between two points without using a coordinate system
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How Does Non-Euclidean Geometry Differ from Euclid's Postulates?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Geometry Challenge: Prove $\angle ADE=\angle BDC$ in Convex Quadrilateral $ADBE$
  • · Replies 3 ·
Replies
3
Views
1K
MHB Computation of bond angles and other angles in tetrahedral
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Geometry problem of interest with a 3-4-5 triangle
  • · Replies 59 ·
2
Replies
59
Views
96K
Suggestions for HS geometry book (proofs)
  • · Replies 14 ·
Replies
14
Views
3K
MHB Prove Angle of Diagonals in Quadrilateral is Degrees
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Resource help for co-ordinate geometry
  • · Replies 4 ·
Replies
4
Views
2K