We will discuss here about the distance properties in some geometrical figures.

1. A triangle ABC is an isosceles triangle if AB = AC or AB = BC or AC = BC.

2. A triangle ABC is an equilateral triangle if AB = BC = CA.

3. A triangle ABC is a right-angled triangle if the sum of the squares of two sides is equal to the square of the third side, i.e.,

AB\(^{2}\) = BC\(^{2}\) + CA\(^{2}\) or BC\(^{2}\) = CA\(^{2}\) + AB\(^{2}\) or AC\(^{2}\) = AB\(^{2}\) + BC\(^{2}\)

4. The distance of any point on a circle from the centre = radius of the circle.

Properties of various types of quadrilaterals

5. A quadrilateral is a parallelogram if its opposite sides are equal. A quadrilateral ABCD is a parallelogram if AB = CD and AD = BC.

6. A quadrilateral is a parallelogram but not a rectangle if its opposite sides are equal and the diagonals are not equal.if its opposite sides are equal.

7. A quadrilateral is a rectangle if its opposite sides are equal and the diagonals are equal. A quadrilateral ABCD is a rectangle if ABCD is a parallelogram and diagonal AC = Diagonal BD.

8. A quadrilateral ABCD is a rhombus if AB = BC = CD = DA.

9. A quadrilateral is a rhombus but not a square if all its sides are equal and the diagonals are not equal.

10. A quadrilateral is a square if all its sides are equal and the diagonals are equal. A quadrilateral ABCD is a square if ABCD is a rhombus and diagonal AC = Diagonal BD.

● **Distance and Section Formulae**

**Distance Formula****Distance Properties in some Geometrical Figures****Conditions of Collinearity of Three Points****Problems on Distance Formula****Distance of a Point from the Origin****Distance Formula in Geometry****Section Formula****Midpoint Formula****Centroid of a Triangle****Worksheet on Distance Formula****Worksheet on Collinearity of Three Points****Worksheet on Finding the Centroid of a Triangle****Worksheet on Section Formula**

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