Question

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

Answer 1

Given

ABC is a triangle D, E and F are respectively the mid-points of sides AB, BC and CA

To prove

∆ ABC is divided into 4 congruent triangles

Proof

D and F are mid-points of sides AB and AC of ∆ ABC     [given]

∴ DF ∥ BC   [Mid-Pt Theorem]

Similarly, we can write DE ∥ AC and EF ∥ AB

Now in DBEF, DF ∥ BE, & DB ∥ EF

Since both pairs of opposite sides are parallel, DBEF is a parallelogram DBEF is a parallelogram & DE is a diagonal

∴ Δ DBE ≅ Δ DFE [Diagonal of a parallelogram divides it into 2 congruent triangles]   ---(1)

Similarly, DFCE is a parallelogram,

∴ Δ DFE ≅ Δ CEF    ---(2)

ADEF is also parallelogram,

∴ Δ ADF ≅ Δ DFE   ---(3)

From (1), (2) & (3) Δ DBE ≅ Δ DFE ≅ Δ CEF ≅ Δ ADF ∴ All 4 triangles are congruent

Check attachment for figure.

Answer 2

Answer:

Here is the answer

Step-by-step explanation:

hope it helped u ✌