The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.
What is Hinge Theorem example?
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 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 are the hinge devices?
A pin, that may or may not be removable, joins the two leaves (or plates) at the hinge’s knuckles.
- Ball Bearing Hinge. …
- Spring-Loaded Butt Hinge. …
- Barrel Hinge. …
- Concealed Hinge. …
- Overlay Hinge. …
- Offset Hinge. …
- Piano Hinge. …
- Strap Hinge.
Why scissor is 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.
Which side of ∆ set is the longest?
The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
Why compass is a Hinge Theorem?
8. Possible answer: The legs of a compass and the length spanned by it form a triangle, but the lengths of the legs cannot change. Therefore any two settings of the compass are subject to the Hinge Theorem.
What is the difference between the altitude rule and the leg rule?
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule! … The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
What do you call a statement that is accepted without proof?
An axiom or postulate is a fundamental assumption regarding the object of study, that is accepted without proof.
What is the sum of complementary angle?
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
What is isosceles theorem?
The isosceles triangle theorem states the following: Isosceles Triangle Theorem. In an isosceles triangle, the angles opposite to the equal sides are equal. Conversely, if the base angles of a triangle are equal, then the triangle is isosceles.
What do you call the longest side of a right triangle?
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.
Which is the shortest side of a right triangle?
The angles in any triangle add up to 180°. In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side.
Which is the shortest side in triangle EFG?
The length of the sides of EFG are 144 cm, 128 cm and 112 cm. The length of the smallest side of QRS is 280 cm.
What is the difference between hinge theorem and 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 …
How does a scissor hinge work?
A scissor hinge can either lift up or drop down, and is used to control the opening of cabinet fronts as well as lids on things like cedar chests, hampers, tool chests, and radiator covers. The hinge opens and holds at a predetermined angle, requiring the application of pressure to close again.
What is inequality theorem?
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. … In other words, as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side, then you know that the sides do not make up a triangle.
What are the 4 styles of hinge called?
The most common hinge used on doors and cabinets, butt hinges have two rectangular-shaped leaves with knuckles in the middle, joined by a pin. There are several types: plain bearing, ball bearing (see above), spring-loaded and rising.
What hinge do you use for full opening?
This type of hinge is also known as a continuous hinge. It runs the entire length of the door. Piano hinges are manufactured with or without holes. These hinges also come in various thicknesses, pin diameters, and knuckle lengths.
What is a butterfly hinge?
: a decorative hinge that has the appearance of a butterfly when the leaves are spread flat.