Justify: why does doors illustrate hinge theorem?
Answers
Step-by-step explanation:
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.
The Hinge Theorem
Suppose you and your friend, Mary, are walking through a haunted house at an amusement park, and you come across a trap door on the ground that you have to go through. You go first by opening the door so that the length of the opening is large enough for you to fit through it. Mary goes second, and has to open the door a bit wider to make the length of the opening large enough for her to fit through.
Do you notice that when the opening length is shorter, the angle at the hinge of the door is smaller than when the opening length is larger? Do you also notice that the door length and the floor length of the door remain the same in both cases, and it's just the opening length and the hinge angle that change? This has great mathematical significance! So great that there is a theorem that explains this phenomenon, and it is appropriately called the hinge theorem.
The hinge theorem states that if two triangles have two congruent sides (sides of equal length), then the triangle with the larger angle between those sides will have a longer third side. This also gives way to the converse of the hinge theorem, which 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.
To illustrate this, think about the trap door again. When we open it, we create a triangle. One side is the door, one side is the floor length of the door, and the third side is the opening length. The wider you open the door, the greater the hinge angle and the greater the opening length.
When it's put like that, it seems like common sense! Let's take a look at using this theorem to compare triangles and in an application!
I HOPE IT WILL HELPFUL TO YOU
Introduction:
The hinge theorem in geometry says that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is greater than the included angle of the second, the third side of the first triangle is larger than the third side of the second triangle.
Step-by-step explanation:
Consider the trap door to demonstrate this. We make a triangle when we open it. The door is on one side, the floor length is on the other, and the opening length is on the third. The bigger the hinge angle and the greater the opening length, the broader the door is opened.
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