Question
Prove that the diagonals of a rectangle bisect each other. Â [4 MARKS]
Answer:
:
Properties: 1 Mark
Proof: 1 Mark
Steps: 2Marks
In a rectangleopposite sides are equal and parallel.
In ΔOADandΔOCB,
∠ODA=∠OBC
[Alternate interior angles; AD∥BC and BDas transversal]
AD = BC [Opposite sides of a rectangle are equal]
∠OAD=∠OCB
[Alternate interior angles; AD∥BC and ACas transversal]
Hence ΔOAD≅ΔOCB [By ASA congruence rule]
Equating the corresponding parts of congruent triangles, we get:
AO = CO
BO = DO
⇒ Diagonals of a rectangle bisect each other.
Was this answer helpful ?
:
Properties: 1 Mark
Proof: 1 Mark
Steps: 2Marks
In a rectangleopposite sides are equal and parallel.
In ΔOADandΔOCB,
∠ODA=∠OBC
[Alternate interior angles; AD∥BC and BDas transversal]
AD = BC [Opposite sides of a rectangle are equal]
∠OAD=∠OCB
[Alternate interior angles; AD∥BC and ACas transversal]
Hence ΔOAD≅ΔOCB [By ASA congruence rule]
Equating the corresponding parts of congruent triangles, we get:
AO = CO
BO = DO
⇒ Diagonals of a rectangle bisect each other.
Was this answer helpful ?
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