Leah is buying curtains for her bedroom window. she wants the certains to hang from the top of the window to the floor. the window is 4 feet high. the bottom of the window is 21/2 feet above the floor. how many inches long should leahs certains be?

Because the window is 4 feet and you need it to cover the window and the floor, you could start with the window. 4 feet at 12 inches per foot is 48 inches already. Then you would add the distance between the window and the floor, 21/2 feet is 10.5 feet. 10.5 * 12 inches is 126 inches. 126+48=174. You need 174 inches. See my pic

Please see attachment.

Solution:

We need to match the column using column proof. Please see the attachment for matching column.

In ΔDOC and ΔBOA

      DO=BO               (Given)

 ∠DOC=∠BOA          (Vertically Opposite angle)

      OC=OA               (Given)

∴   ΔDOC ≅ ΔBOA   by  SAS congruence property

     ∠1=∠2  and  AB=DC     By CPCTE

Thus, AB||DC   (∠1 and ∠2 are alternate angles equal then lines parallel)

ABCD is a parallelogram. ( If two sides equal and parallel then a parallelogram.

Below is matched table.

DO = OB, AO = OC ⇒ Given      

∠ DOC =∠ AOB      ⇒ Vertical angles are equal

∆COD ≅ ∆AOB⇒  SAS             CPCTE

∠1 = ∠2,  AB = DC⇒  CPCTE          

AB||DC                 ⇒  If alternate interior angles =, then lines parallel

ABCD is a parallelogram ⇒ If two sides = and ||, then a parallelogram

Please see attachment for figure and matching.