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
• B. ASA
• C. SAS
• D. RHS

Answer 1

Answer: (A), (B), (C), (D)

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

$\angle$BAC = $\angle$DCA (alternate angles)
side CA is common
$\angle$ACB = $\angle$CAD (alternate angles)
...ASA criteria

AB = AD (side of the square)
$\angle$ABC = $\angle$ADC = right angle (angle formed by two sides of a square)
BC = DC (side of the square)
...SAS criteria

$\angle$ABC = $\angle$ADC = right angle (angle formed by two sides of a square)
side CA is common (hypotenuse)
AB = AD (sides of the square)
...RHS criteria