Question

Describe all Theorem's of Triangle [Class = 8th ICSE]

Answer 1

Suppose a line XY is parallel to side BC.  AB is a transversal that cuts line XY and AB, at A and B, respectively.  As the alternate interior angles are equal, .  Also, .   form a linear pair, and their sum is . 

Exterior angle property:

An exterior angle of a triangle is equal to the sum of its opposite interior angles. 

Eg: In the figure here, ∠4 is called the exterior angle        
to triangle ABC, and ∠4 = ∠1 + ∠2.

The sum of the lengths of any two sides of a triangle is greater than the third side.





In a right-angled triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called its legs.

Pythagorean theorem:

In a right-angled triangle, the square of the hypotenuse is    
equal to the sum of the squares of the other two legs.
 a2 = b2 + c2



 Converse:

If the Pythagoras property holds, then the triangle must be right-angled. That is, if there is a triangle such that the sum of the squares on two of its sides is equal to the square of the third side, then it must be a right-angled triangle.

Answer 2

congruent figures always coinside by superposition it if two Triangles are congruent then by placing One triangle over the other day coinside exactly