Question

triangles important theroms class 9
explain it...​

Answer 1

Answer:

given: inΔ A B C ,Let D and E be the midpoints of AB and AC. Suppose that you join D and E:.

TPT:

Proof: Through C, draw a line parallel to BA, and extend DE such that it meets this parallel at F, as shown below:

Compare  Δ A E D  with  Δ C E F :

1. AE = EC (E is the midpoint of AC)

2.  ∠ D A E  =  ∠ F C E  (alternate interior angles)

3.  ∠ D E A  =  ∠ F E C  (vertically opposite angles)

By the ASA criterion, the two triangles are congruent. Thus, DE = EF and AD = CF. But AD is also equal to BD, which means that BD = CF (also, BD || CF by our construction). This implies that BCFD is a parallelogram. Thus,

1. DF || BC è DE || BC

2. DE = EF = ½(DF) = ½(BC) èDE = ½(BC)