Question

ABCD is a quadrilateral where AB ll DC.
A) show that triangles ABC and ADC are congruent.
B) now deduce that ABCD is a parallelogram.

Answer 1

The Triangles ABC and ADC are congruent by the SAS test

• Seg AD ≅ Seg BC ..... (The Opp. sides of the Rhombus are ≅)
• ∠ADC≅ ∠ ABC ..... (The Opp. Angles of the Rhombus are ≅ )

• Seg AB ≅ Seg DC ...... (The Opp. sides of the Rhombus are ≅)

As we go through the properties of the ║gm (Parallelogram),

• The opp. sides of the parallelogram are ≅
• The opp. angles of the parallelogram are ≅
• The Diagonals of the Parallelogram are ≅

These all properties of the parallelogram are similar to the properties of the properties that of the rhombus.

Therefore, we can say that the Quadrilateral ABCD is a Parallelogram.