Why is it called the hinge theorem?

Why is it called the 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. The sides described in this theorem are the jaw lengths of the alligator with the “hinge” being at the corner of the alligator’s mouth (point A or D).

What is Triangle Inequality theorem 2?

The Formula. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

What are the inequalities in two triangle?

The theorem states that if two sides of triangle A are congruent to two sides of triangle B, and the angle between them is bigger in triangle A, then the third side of triangle A is bigger. If the angle between them is smaller in triangle A, the third side of triangle A is smaller.

What is converse Pythagorean Theorem?

The converse of the Pythagorean Theorem says that if a triangle has sides of length a, b, and c and if a^2 + b^2 = c^2 then the angle opposite the side of length c is a right angle.

What is SSS Inequality theorem?

The SSS Inequality Theorem states: If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer 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 exterior angle Inequality theorem?

Geometry. The exterior angle of a triangle will always be greater than the two remote interior angles. In other words, the measure of the red angle is greater than that of the blue angle or the green angle.

How do you write a triangle inequality?

Any side of a triangle must be shorter than the other two sides added together. If a side is equal to the other two sides it is not a triangle (just a straight line back and forth)….When the three sides are a, b and c, we can write:

1. a < b + c.
2. b < a + c.
3. c < a + b.

How to learn triangle inequality theorem in high school?

Focusing on the triangle inequality theorem, the high school worksheets feature adequate skills such as check if the side measures form a triangle or not, find the range of possible measures of the third side, the lowest and greatest possible whole number measures of the third side and much more.

How to reaffirm the triangle inequality theorem?

Reaffirm the triangle inequality theorem with this worksheet pack for high school students. The length of a side of a triangle is less than the sum of the lengths of the other two sides. Add up the two given sides and subtract 1 from the sum to find the greatest possible measure of the third side.

How do you find the sides of a triangle?

Figure out if the given lengths form the sides of the triangle by applying the triangle inequality theorem. Add any two lengths, if their sum is greater than the third side, then the sides form a triangle. Compute the range of possible measures of the third side of the triangle in this set of printable worksheets.

How do you prove triangles are congruent?

1. If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then prove that the included angle of the first triangle is larger than the included angle of the second triangle. 2. In triangles ABC and DEF, we have