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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)
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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.
संबंधित प्रश्न
In a parallelogram ABCD, the diagonals bisect each other at O. If ∠ABC = 30°, ∠BDC = 10° and ∠CAB = 70°. Find:
∠DAB, ∠ADC, ∠BCD, ∠AOD, ∠DOC, ∠BOC, ∠AOB, ∠ACD, ∠CAB, ∠ADB, ∠ACB, ∠DBC and ∠DBA.
Which of the following statement is true for a rectangle?
It has two pairs of equal sides.
Which of the following statement is true for a rectangle?
Its diagonals bisect each other.
Which of the following statement is true for a rectangle?
Its diagonals are perpendicular.
State with reason whether the following statement is ‘true’ or ‘false’.
Every parallelogram is a rectangle.
Draw a rectangle ABCD such that l(AB) = 6.0 cm and l (BC) = 4.5 cm.
If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.
For which of the following figures, diagonals are equal?
In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.
A rectangular MORE is shown below:
Answer the following questions by giving appropriate reason.
- Is RE = OM?
- Is ∠MYO = ∠RXE?
- Is ∠MOY = ∠REX?
- Is ΔMYO ≅ ΔRXE?
- Is MY = RX?
