Question

The diagonal from B to D is drawn in parallelogram ABCD. Which of the following methods can NOT be used to prove $△DAB\cong △BCD$

• A. SSS
• B. SAS
• C. SSA
• D. ASA

Answer 1

Answer: (D)

Consider $△ABD$ and $△CBD$

$AD=BC,AB=CD$ ..... In a parallelogram, opposite sides are equal

$BD$ is the common sides for both triangles

$⟹SSS$ postulate proves that they are congruent

$AD=BC,AB=CD$ ......... In a parallelogram, opposite sides are equal

$\angle DAB=\angle DCB$ ........ In a parallelogram, opposite angles are equal

$⟹SAS$ postulate proves that they are congruent

The $SSA$ Postulate does not exist because an angle and two sides does not guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non included angle, then triangles are $NOTNECESSARILY$ congruent.

$\angle BDC=\angle DBA$ -----------alternate angles : $AB||DCandDB$ is the transversal

$BD$ is the common side

$\angle ADB=\angle DBC$ -----------alternate angles : $AB||DCandDB$ is the transversal

$⟹ASA$ postulate proves that they are congruent