Question

Prove that points (0,0) , (5,5) ,and (-5,5) are the vertices of a right isosceles triangle .

Answer 1

Please refer the above photograph for the used process.


KEY POINTS TO REMEMBER :-


☸️ DISTANCE FORMULA :-

It is the formula used for finding the distance between two given points in the Cartesian plain.

The representation of the formula is :-

$d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$
Where d is the distance between the two points.



☸️ CONVERSE OF PYTHAGORAS THEOREM :-

The theorem states that
If the sum of squares of any two sides of a triangle is equal to the square of third side, The triangle is a right angled triangle.



☸️ PROPERTIES OF ISOSCELES TRIANGLE :-

(i) Any two sides of this type of triangle is equal.

(ii) The angles corresponding to the equal sides are also equal

(iii) If the triangle is an isosceles right triangle, The other two angles will be equal to 45°

(iv) The median of the isosceles triangle is also the perpendicular bisector of the triangle.

(v) The triangles formed by the median are congruent to each other as well as similar to each other.




Thanks!