How can the Hinge Theorem be used in real life?
The plane on the triangle with the larger included angle is farther from the airport, because the hinge theorem says the third side will be larger in this triangle. Because 113 > 48, the hinge theorem tells us that AD is longer than AC, so Airplane 2 is closer to the airport. This hinge theorem is quite useful!
What is the example of Hinge Theorem?
The Hinge Theorem states that in the triangle where the included angle is larger, the side opposite this angle will be larger. It is also sometimes called the “Alligator Theorem” because you can think of the sides as the (fixed length) jaws of an alligator- the wider it opens its mouth, the bigger the prey it can fit.
Why scissors is a Hinge Theorem?
This theorem is called the “Hinge Theorem” because it acts on the principle of the two sides described in the triangle as being “hinged” at their common vertex.
What is the Hinge Theorem in simple terms?
The Hinge Theorem states that if two sides of two triangles are congruent and the included angle is different, then the angle that is larger is opposite the longer side.
How does Hinge Theorem work?
In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
How can you apply illustrating theorems on triangle inequalities in real life situation?
Triangle Inequality Proof We can additionally conclude that in a triangle: Since the sum of any two sides is greater than the third, then the difference of any two sides will be less than the third. The sum of any two sides must be greater than the third side.
What is converse hinge Theorem?
The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second …
What is the importance of learning triangle inequality theorems?
What are the Applications of Triangle Inequality? The triangle inequality theorem is one of the most important mathematical principles that is used across various branches of mathematics. It is a useful tool for checking if a given set of three dimensions will form a triangle or not.
How do we apply theorems on triangle inequalities in our real life situation?
In real life, civil engineers use the triangle inequality theorem since their area of work deals with surveying, transportation, and urban planning. The triangle inequality theorem helps them to calculate the unknown lengths and have a rough estimate of various dimensions.
What is the hinge theorem converse based on?
The SSS inequality theorem is the converse of the hinge theorem: if two sides of two triangles are congruent, but the third side on one is shorter than on the other, we know that the corresponding angle is also smaller.
How do you know if it is a Hinge Theorem?
The Hinge Theorem states that if two sides of two triangles are congruent and the included angle is different, then the angle that is larger is opposite the longer side. In the image below, we can see that since angle D is larger than angle A, side EF is longer than side BC.
What is the hinge theorem is based on?
In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
What is the hinge theorem Converse used to show?
The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
What is the converse of the hinge theorem?
Converse. The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
What are the right angles congruence theorem?
Right Triangle Congruence Theorem A plane figure bounded by three finite line segments to form a closed figure is known as triangle. A right angled triangle is a special case of triangles. In a right angled triangle, one of the interior angles measure 90°.Two right triangles are said to be congruent if they are of same shape and size.