Q. 16

# ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A,B and C. (The dotted lines are drawn additionally to help you).

Answer :

Draw lines AD and DC such that AD||BC, AB||DC

AD = BC, AB = DC

ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90^{o}

In a rectangle, diagonals are of equal length and also these bisect each other

Hence, AO = OC = BO = OD

Thus, O is equidistant from A, B, and C

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If the diagonals of a rhombus are 12 cm and 16 cm, find the length of each side.

RD Sharma - MathematicsWhich of the following statements are true for a square?

(ii) It has all its sides of equal length.

(iii) Its diagonals bisect each other at right angle.

(v) Its diagonals are equal to its sides.

RD Sharma - MathematicsConstruct a rhombus whose diagonals are of length 10 cm and 6 cm.

RD Sharma - MathematicsWhich of the following statements are true for a rectangle?

(i) It has two pairs of equal sides.

(ii) It has all its sides of equal length.

(iii) Its diagonals are equal.

(iv) Its diagonals bisect each other.

(v) Its diagonals are perpendicular.

(vi) Its diagonals are perpendicular and bisect each other.

(vii) Its diagonals are equal and bisect each other.

(viii) Its diagonals are equal and perpendicular, and bisect each other.

(ix) All rectangles are squares.

(x) All rhombuses are parallelograms.

(xi) All squares are rhombuses and also rectangles.

(xii) All squares are not parallelograms.

RD Sharma - Mathematics