What is the triangle inequality theorem?
triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
When triangle inequality is an equality?
In the Euclidean case, equality occurs only if the triangle has a 180° angle and two 0° angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shortest distance between two points is a straight line.
What are triangle theorems?
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent….Angles:
| Right Angles | All right angles are congruent. |
|---|---|
| Vertical Angles | Vertical angles are congruent. |
| Triangle Sum | The sum of the interior angles of a triangle is 180�. |
Why is Cauchy Schwarz inequality?
The Cauchy–Schwarz inequality is used to prove that the inner product is a continuous function with respect to the topology induced by the inner product itself.
How many triangle theorems are there?
Triangle theorems are basically stated based on their angles and sides. Triangles are the polygons which have three sides and three angles….
| MATHS Related Links | |
|---|---|
| Highest Common Factor | Types Of Polygon |
| Line Segment | Trigonometric Equations |
| Area And Circumference Of A Circle | Logarithm Problems |
Which of the following is Cauchy Schwartz inequality?
( ∑ i = 1 n a i 2 ) ( ∑ i = 1 n b i 2 ) ≥ ( ∑ i = 1 n a i b i ) 2 . Not only is this inequality useful for proving Olympiad inequality problems, it is also used in multiple branches of mathematics, like linear algebra, probability theory and mathematical analysis. …