Is the triangle sum theorem true on the surface sphere? Explain why or why not.

Answer: No, the triangle sum theorem is not true for a sphere surface.

Explanation:

Consider 3 cities A,B,C at the following locations

The placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.

No, the triangle sum theorem is not true on the surface sphere.

The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.

Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,

A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.

Hence, there exists no such triangle on the surface of a sphere.

For more references on triangle sum theorem, click;

https://brainly.com/question/2995226

#SPJ5

In a factory, eggs are packaged in groups of 12 per box.How many full boxes of eggs can the factory make with 2321 eggs?

14.L
Marcy walked 37 miles on Saturday. On
Sunday, she walked 0.25 more miles than
she did on Saturday. How many total miles
did she walk over the weekend?

Give your final answer as a fraction in simplest form

the correct answer is in fact C , I just took the test

Is the point (1,2) on the graph of f(x)=3x-1
(Show full working) ​

Nikko runs 6 miles a day and 3 days a week. How many weeks will it take Nikko to run 198 miles?

Austin earns $9.75 an hour at a part-time job, and earns $12 each time mowing lawns in the neighborhood. They graph the amount of hours worked at the part-time job (X) and the number of lawns mowed (Y) to determine how to earn more than $300. Which type of boundary line should be used in the graph?HELP!

Which expression is not equivalent to 3 ∙ S ∙ R?

A) 3 + S + R

B) 3SR

C) 3RS

Choose a rational function with a removable discontinuity. A f(x)=x+1x+2f\left(x\right)=\frac{x+1}{x+2}f(x)= x+2 x+1 ​ B g(x)=xx2g\left(x\right)=\frac{x}{x^2}g(x)= x 2 x ​ C h(x)=2x2−2x+1h\left(x\right)=\frac{2}{x^2-2x+1}h(x)= x 2 −2x+1 2 ​ D j(x)=2xx2−1j\left(x\right)=\frac{2x}{x^2-1}j(x)= x 2 −1 2x ​

please help me i will mark as brainliest​

Can some one help me with this please :)

Steve is an under armor sweatshirt with a normal price of $40 but he uses a 10% off coupon how much does he say if I using this coupon?

Write 45 as a product of three primes

ViperDrink
6 12-ounce cans for $2.19
or
Totally Soda
4 16-ounce bottles for $2.19

The perimeter of the yard is 390 feet. The width of the yard is 5 feet less than the length.

Equation:
What is the length of the yard?
What is the width of the yard?
What is the area of the yard?

Answer in full

The current population of a town is 32,000 and town officials estimate that the population will continue to grow by 900 every year.​

One challenge of federalism is that

power and authority are concentrated in the central government and can take away people’s rights
sometimes officials from different levels of government disagree on who should be in charge of a situation
local governments have the most power, which creates problems for trade with other nations
officials from state governments have too many rules to follow to be effective leaders

EXPERTS WHERE YALL AT?
1. 7s - 3b + 8 - 4, when s=7 and b=4
2. 6r - 10/r , when r=5 and z=3
3. 3c² + d³, when c = 1 and d=2
4. 5x², when x = 3

Gladys classifies the following system of equations.
y = 6x + 2
y = 6x + 1
Select Correct or Not correct for each statement.
Statement
Correct
Not correct
o
O
The system is inconsistent because the slopes are the same and the lines are different.
The system is dependent because the y-intercepts are different.
O
O

Please Help!! Asap!!

A local club team is holding tryouts for six spots on the soccer team. Since there is not much time before a very important tournament they need to select the best players. Which method would be the best to ensure they select the "most talented" soccer players?


A. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top six from the list.


B. The first day of tryouts they select the first six that show up as they figure those are the most eager for a spot.


C. They place all of the names of the people trying out in a hat and then select six out of the hat. Those are the ones that are chosen.


D. They watch the players during tryouts and then put them on a list in order from the most skilled to the least skilled and then select the top three and the bottom three from the list.

Bruce spent $30 on lunch. If he had $55 in his wallet, what percent of this money did he spend on lunch?

(PERSON WHO EXPLAINS THE BEST AND ANSWERS CORRECTLY GETS MARKED BRAINLIEST)

Given: g(x) = Vx – 4 and h(x) = 2x - 8.
-
What is g(h(10))?
o 2/2
N
O V6
0 V6-8
02-76 - 8
-
can anyone pls help

iready math, i need to answer asap

20 points!!!1
PLss help me

expand and simplify 3(f+3) + 2 (f+6)

REASONING You can paint 75 square feet of a surface every 45 minutes. Determine how long
it takes you to paint a wall with the given dimensions.
9 ft x 9 ft
It will take you___
minutes to paint the wall.

Will give brainliest!

3(3−3)=2(+3)−30 how do I do this???? I'm in 10th grade and this confuses me every time.

look at me - on me look at me - on me yeah

what is 5*2+4*6+10+123+(8)-1

ASAP!!!The 70th term of the arithmetic sequence -12,-8,- 4, ... is:
A. 74
B.264
C.268
D.270​