Given: A right triangle DEF, in which A, B,C are mid points of DE , EF, and FD respectively. BC=6 cm, AC= 5 cm, BA=4 cm
Solution:
1. Perimeter of triangle ABC=AB+BC+CA=6+5+4=15 cm
But it is given that perimeter of triangle ABC is 12 cm.So, this is incorrect statement.
2. As we know line segment joining the mid point of two sides of triangle is parallel to third side and is half of it.
AB║DF and AB=1/2 DF, BC║DE and BC=1/2 DE, AC║EF,and AC=1/2EF
∴Quad.ABCF, Quad.CBAE, Quad.DABC is a parallelogram, and diagonal of parallelogram divides it into two congruent triangles.
ΔABC≅ΔBCF≅DAC≅ABE
Area(ΔDEF)=4×Area(ΔABC)
→ Area of triangle ABC to area of triangle DEF is 1/4.
