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 rightangled 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.
10th Grade Math
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