MHB What is the proof for angle equality?

  • Thread starter Thread starter paulmdrdo1
  • Start date Start date
  • Tags Tags
    Angle Proof
Click For Summary
When two lines intersect, they create opposite angles that are equal due to the properties of vertical angles. This relationship is grounded in the theorem stating that angles formed by intersecting lines are equal when their sides are perpendicular. The proof of angle equality can be derived from this theorem, demonstrating both the "how" and "why" of their equality. Understanding this fundamental concept is essential in geometry. The discussion highlights the importance of recognizing the properties of intersecting lines in proving angle relationships.
paulmdrdo1
Messages
382
Reaction score
0
I've been searching over the internet and geometry books for the proof of the relationship of these two angles but I couldn't find one. Can you tell me the "how" and "why" of their equality. thanks and regards!
 

Attachments

  • equal angles.png
    equal angles.png
    3.2 KB · Views: 85
Mathematics news on Phys.org
Use the fact that when two lines intersect, opposite angles are equal. The result then follows.
 
Check post #5.

http://mathhelpboards.com/trigonometry-12/equality-angles-11593.html

"There is a theorem saying that two angles whose sides are mutually perpendicular are equal. "
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

B I've been trying to understand the proof for the binomial theorem
Replies
6
Views
2K
I Proof for interpolating polynomial and error approximation
Replies
6
Views
2K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K
I Prove that solid angle of any closed surface is 4pi
Replies
5
Views
9K
Suggestions for HS geometry book (proofs)
Replies
14
Views
2K
What is the difference between the two sine rules for resultant vector?
Replies
4
Views
2K
MHB Proving the Angle-Angle-Side Theorem
Replies
1
Views
2K
A How did Saccheri prove Euclid's Fifth Postulate?
Replies
6
Views
3K
I Question about Euclid's parallel postulate (5th postulate).
Replies
16
Views
4K
MHB Find the Bearing from A to C & Angle B: Solve Here
Replies
3
Views
2K