Answer:
The Proof is below.
Step-by-step explanation:
Given:
ABCD is a Parallelogram
Construction:
Draw diagonal AC
To Prove:
AB ≅ CD
BC ≅ DA
Proof:
ABCD is a Parallelogram. ...............Given
BC || DA ........Opposite sides of Parallelogram are Parallel
AB || CD ........Opposite sides of Parallelogram are Parallel
Now,
In ΔABC and ΔCDA
∠BCA ≅ ∠DAC ...……….{Alternate Angles are equal since BC || DA}
∠BAC ≅ ∠DCA …………..{Alternate Angles are equal since AB || CD}
AC ≅ AC …....…….{Reflexive Property}
ΔABC ≅ ΔCDA ..........….{By Angle-Side-Angle Congruence Postulate}
AB ≅ CD ....{Corresponding parts of Congruent Triangles are Congruent}
BC ≅ DA ....{Corresponding parts of Congruent Triangles are Congruent}
