Question

I need all the proofs and statements!!

Answer 1

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}