Question

in triangle ABC,D and E are mid points of sides BC and AC respectively. Find the length of DE.Prove the DE=1/2 AB?

Answer 1

5) i.e. self PB || seg CR. ... ( from 4 & A-P-B)

6)Seg PB = Seg CR

7) But AP= PB. ... ( given)

8)so PB= CR. ... ( from 6&4)

9)Thus quadrilateral PBCR is a parallelogram. ... (from 5&8 and opposite side are congruentand parallel test)

10) so Seg PR|| Seg PC. ... ( definition of parallelogram)

11) i.e. Seg PQ || Seg B.C. ... ( from 10 P-Q-R)

12) PR=BC. ... (opposite side of parallelogram )

13)1/2PR=1/2BC. ... (multiplying by 1/2)

14) But 1/2 PR=PQ

15) PQ = 1/2 BC

PROVED