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Each diagnol divides the rectangle into two equal congruent triangles
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Let us assume a rectangle ABCD with diagonal AC ( see figure )
Given:
- ABCD is a rectangle.
To Prove:
- ∆ADC is congruent to ∆ABC
PROOF
In ∆ADC and ∆ABC,
AC = AC ( Common side )
angle DAC = angle BCA ( Alternate Interior Angles , Since AD || BC and AC as transversal )
AD = BC ( Opposite sides of a rectangle are equal )
•°• By SAS criteria,
∆ADC is congruent to ∆ABC
Hence, Proved.
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