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# D and E are the mid-points of the sides AB and AC respectively of ∆ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is

a. ∠DAE = ∠EFC

b. AE = EF

c. DE = EF

d. ∠ADE = ∠ECF.

**Solution:**

In ∆ADE and ∆CFE,

Let us assume DE = EF

As E is the mid-point of AC

AE = CE

If DE = EF

∠AED = ∠FEC [vertically opposite angles]

From the SAS congruence rule

∆ADE ≅ ∆CFE

AD = CF [c.p.c.t]

∠ADE = ∠CFE [c.p.c.t]

We know that alternate angles are equal

AD || CF

Therefore, we need additional information which is DE = EF.

**✦ Try This: **The figure obtained by joining the mid-points of the adjacent sides 12 cm and 6 cm a. a rhombus, b. a rectangle, c. a square, d. any parallelogram

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 14**

## D and E are the mid-points of the sides AB and AC respectively of ∆ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is , a. ∠DAE = ∠EFC, b. AE = EF, c. DE = EF, d. ∠ADE = ∠ECF

**Summary:**

D and E are the mid-points of the sides AB and AC respectively of ∆ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need additional information which is DE = EF

**☛ Related Questions:**

- A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between t . . . .
- ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is a. 40º, b. 45º, c. 50º, d. 60º
- The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in or . . . .

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