A square is divided into two parts by drawing one of its diagonal. What all congruency criteria can be used to prove the two triangles formed congruent?
A
SSS
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B
ASA
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C
SAS
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D
RHS
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Solution
The correct options are A SSS B ASA C SAS D RHS
Line AC is a diagonal of the square ABCD
Consider △ABC and △ADC
CA = CA ( common) AB = AD (side of the square) BC = DC (side of the square) ...SSS criteria
∠BAC = ∠DCA (alternate angles) side CA is common ∠ACB = ∠CAD (alternate angles) ...ASA criteria
AB = AD (side of the square) ∠ABC = ∠ADC = right angle (angle formed by two sides of a square) BC = DC (side of the square) ...SAS criteria
∠ABC = ∠ADC = right angle (angle formed by two sides of a square) side CA is common (hypotenuse) AB = AD (sides of the square) ...RHS criteria