Question

Given: ABCD is a parellelogram. Prove: AB=CD and BC=DA

Answer 1

Answer:

Step-by-step explanation:

We have given a parallelogram ABCD.

For a parallelogram,

Opposite pair of sides are parallel to each other.

i.e AD is parallel to BC and AB is parallel to CD.

From the attached figure,

∡1 = ∡4  and  ∡2 = ∡3    {If two parallel lines cut by a transversal line then alternate interior angles are congruent }

Next, AC ≅ AC  {Reflexive identity}

hence, ΔABC ≅ ΔCDA   , By Angle-Side-Angle(ASA) congruent property of triangle.

Therefore, AB = CD  and AD = BC   {Proved}

Answer 2

Answer:

1)Abcd is a parallelogram,1)given,2)AB||CD,2)Def of Parallelogram,3$BC||DA,3$Def of parallelogram,4)draw AC,4)Unique line prostate,5)<BCA and <DAC are alt. interior angles,5) Def of alt. Int. angles,6)<DCA and <BAC are alt interior angles ,6)def of alt interior angles,7)<BCA=<DCA,7) Alternate interior angles theorem

8)<BAC=<DCA,8)Alternate interior angles theorem,9)AC=AC,9)Reflexive property,10)ABC=CDA,10)ASA,11)AB=CD,11)CPCTC,12)BC=DA,12)CPCTC