Question

In triangle ABC, D, E, F are respectively the mid-points of sides AB, BC and CA. Show that triangle ABC is divided into four congruent triangles by joining the mid-points D, E and F.

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irrelevant ans will be repoted​

Answer 1

Answer:

Let's draw the triangle (I used ms paint for the figure)

Now, using midpoint theorem in ΔBAC, we can observe that DF║BC.

Using midpoint theorem in ΔACB, we can observe that FE║AB.

Using midpoint theorem in ΔCBA, we can observe that DE║AC.

Now, we have proved above that  DF║BC and DE║AC. Thus, EDFC is a parallelogram. And we know that the diagonal of a parallelogram form two congruent triangles. In ║gm EDFC, the diagonal FE form two triangles ΔDFE and ΔFCE, and they are congruent, that is,

ΔDFE≅ΔFCE.........(1)

Similarly,

ΔAFD≅ΔDFE...........(2)

ΔBDE≅ΔDFE.............(3)

From (1), (2), and (3), we can say that:

ΔDFE≅ΔAFD≅ΔFCE≅ΔBDE

Thus, ΔABC is divided into four congruent triangles if we join the mid-points D, E and F.

HOPE THIS HELPS :D

Answer 2

Answer:

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