prove that the diagonals of a rectangle are equal
Answers
Answered by
20
Hey there !
Solution:
Refer to the attachment for diagram.
Given : ABCD is a rectangle.
To Prove : AC = BD
Construction : Join AC and BD
Proof :
Consider Δ ADC and Δ BCD
We know that, in a rectangle opposite sides are equal and all the angles are 90°. Hence,
AD = BC ( S )
∠ADC = ∠BCD ( A )
CD = CD ( S ) [ Common Side ]
Therefore by SAS Congruence Criterion, Δ ADC ≅ Δ BCD. By CPCT, AC = BD.
Hence the diagonals are equal.
Hence Proved !
Hope it helped !
Attachments:
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Answered by
9
Step-by-step explanation:
Given:
- A rectangle ABCD in which AC and BD are Diagonals.
To Prove:
- Diagonals are equal i.e AC = BD
Proof: In ∆ABD & ∆BAC , we have
- AB = BA { These sides are common in both triangles }
- ∠A = ∠B { Each side of a rectangle is of 90° }
- AD = BC { Opposite Sides of a rectangle are equal to each other }
∴ ∆ABD ≅ ∆BAC ( By Side Angle Side SAS criteria )
Hence, BD = AC
Attachments:
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