MHB Can triangles with the same side lengths have different angles?

  • Thread starter Thread starter akarikairi
  • Start date Start date
  • Tags Tags
    Angles
akarikairi
Messages
6
Reaction score
0
△ABC has side lengths 4, 4, and 7.
Is there another triangle with the same side lengths but different angles?

I get a lot of questions like these, and I don't know how to judge whether or not they are true or false. Drawing them on paper doesn't always help me either, but I do try to - to get a visual representation of the questions.
 
Mathematics news on Phys.org
Hi akarikairi,

If there was another triangle with the same side lengths, then by SSS the two triangles would be congruent. Then by CPCTC the corresponding angles are congruent. So there is no triangle with the same side lengths as ABC but with different angles.
 
Thank you for the explanation! This is very helpful.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Difference of angles in a triangle
Replies
4
Views
1K
B Understanding the Pythagorean Theorem
Replies
38
Views
3K
MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle
Replies
2
Views
2K
MHB What is the smallest side length BC of triangle ABC with fixed angle and area?
Replies
2
Views
1K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
Replies
1
Views
1K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
Replies
2
Views
1K
I Chiral symmetries in E[SUP]^n[/SUP]
Replies
1
Views
2K
MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
Replies
2
Views
2K
MHB Calculating Triangle Side Length with Known Angles and Radius
Replies
2
Views
1K
MHB Act.ge.5 third angle of triangle
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top