Given: AD ABC and AD || BC
Prove: ABCD is a parallelogram.

We don't get all the menus so we'll have to wing it.

AD ≅ BC   Given

AD || BC    Given

AC ≅ AC   Reflexive property

∠DAC ≅ ∠BCA      Alternate interior angles (of a transverse of parallel lines)

ΔDAC ≅ ΔBCA     SAS (side-angle-side)

∠DCA ≅ ∠BAC     CPCTC  (corresponding parts...)

CD || AB               Converse of alternate interior angles theorem

ABCD is a parallelogram.        Def parallelogram (AD || BC and CD || AB)

d

step-by-step explanation:

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584