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Question

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

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