Triangle:- A polygon with three edges, three vertices and three angles is called Triangles. A triangle with vertices A, B, and C is denoted by ∆ABC.
Existence of a triangle
A Triangle Is Exist If
* If sum of lengths of any two sides side is greater than third side.
AB + BC > AC
BC + AC > AB
AB + AC > BC
A Triangle is not possible if sum of lengths of any two sides side is less than or equal to third side.
*1. If sum of lengths of any two sides side is less than to third side.
AB + BC < AC
BC + AC < AB
AB + AC < BC
*2. If sum of lengths of any two sides side is equal to third side.
AB + BC = AC
BC + AC = AB
AB + AC = BC
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A Triangle Is Exist If
* If each of the angles is positive.
* If the sum of the all three angles is Supplementary (180°).
∠A + ∠B + ∠C = 180°
* It is also known as Angle Sum Property Of A Triangle so that we can say it in short ASPOT.
* A Triangle is not possible if sum of all the three angles is less than or more than 180°.
*1 A Triangle is not possible if sum of all the three angles is less than 180°.
∠A + ∠B + ∠C < 180°
*2 A Triangle is not possible if sum of all the three angles is more than 180°.
∠A + ∠B + ∠C > 180°
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Side Angle Relationship
(A). The side opposite to the largest angle of a triangle is the largest and opposite to smallest is smallest.
*1 ∠B is Greater than ∠A & ∠C
then
Side AC opposite to ∠B is Greater than AB & BC
*2 ∠A is Smaller than ∠B & ∠C
then
Side BC opposite to ∠A is smaller than AB & AC
(B) The angle opposite to the largest side of a triangle is the largest and opposite to smallest is smallest.
*1) Side AC opposite to ∠B is Greater than AB & BC
than
∠B is Greater than ∠A & ∠C
*2) Side BC opposite to ∠A is smaller than AB & AC
than
∠A is Smaller than ∠B & ∠C
then
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Exterior Angle Property Of A Triangle (ExAPOT)
Any exterior angle of the triangle is equal to the sum of its interior opposite angles.
∠1 = ∠3 + ∠4
This property of triangle is called the Exterior Angle Property Of A Triangle (ExAPOT).
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SOAEAT
Sum of all exterior angle of the triangle is equal to 360°.
∠1 + ∠2 + ∠3 = 180°. [by ASPOT]
or
∠7 + ∠8 + ∠9 = 360° [by SOAEAT]
Part 1
Part 2
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Special Names Of The Sides Of The Triangle.
Hypotenuse :- Side opposite to right angle is called Hypotenuse.
We also used this name for opposite side of a given angle.
Base :- Horizontal side of a triangle is known as base.
Base is the adjacent side of a given angle.
Perpendicular :- Non-horizontal side of a triangle is known as Perpendicular.
Perpendicular is the other adjacent side of a given angle.
Perimeter: The sum of the lengths of all the three sides of a triangle is called perimeter.
Perimeter = AB + BC + AC
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