Theorem 6.1 NCERT Class 10 Maths Chapter 6 Triangles

Theorem 6.1 NCERT Class 10 Maths Chapter 6 Triangles

Theorem 6.1:

Theorem 6.1 says that if we draw a line parallel to a side of the triangle; this parallel line divides the other two sides of the triangle in equal ratio.

AD/DB = AE/EC

Proof:

In ΔADE and ΔBDE, the height of the triangle is the same; similarly in ΔADE and ΔCDE height is the same.  We can find the answer if we can correlate them.

Area of ΔADE = 1/2*AD* EN

Similarly, Area of ΔBDE = 1/2*BD*EN

The ratio of areas

Ar(ΔADE)/Ar(ΔBDE) = AD/BD   (1)

Similarly in triangle ΔADE and ΔCDE,

The ratio of areas

Ar(ΔADE/Ar(ΔCDE)= AE/EC   (2)

Now, Area of ΔBDE  and ΔCDE are the same as they have the same base DE and a common height. (3)

So, AD/BD = AE/EC.

Next: Converse of theorem 1: Theorem 6.2