Advertisements
Advertisements
प्रश्न
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)
उत्तर
ABCD is a rectangle as opposite sides are equal and parallel to each other, and all the interior angles are 90º.
In a rectangle, diagonals are of equal length and also these bisect each other.
Since MBC is right-angled at B. So ∠D = 90°, AD||BC and AB||DC
ABCD is a rectangle where AB = CD and AD=BC
AC and BD are the diagonals which bisect each other.
Hence, AO = OC = BO = OD
Thus, O is equidistant from A, B, and C.
APPEARS IN
संबंधित प्रश्न
The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.
The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.
In the following figure, BDEF and DCEF are each a parallelogram. Is it true that BD = DC? Why or why not?
Which of the following statement true for a square?
Its diagonals are equal to its sides.
In a rectangle ABCD, prove that ∆ACB ≅ ∆CAD.
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
Adjacent sides of a rectangle are 7 cm and 24 cm. Find the length of its diagonal.
In a rectangle ABCD, AB = 25 cm and BC = 15. In what ratio does the bisector of ∠C divide AB?
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD
Construct a rectangle whose one side is 3 cm and a diagonal equal to 5 cm.
