Home
Class 9
MATHS
D, E and F are the mid-points of the sid...

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral `Delta`ABC. Show that `Delta`DEF is also an equilateral triangle.

Text Solution

AI Generated Solution

To show that triangle DEF is also an equilateral triangle, we will follow these steps: ### Step 1: Understand the Given Information We have an equilateral triangle ABC, where D, E, and F are the midpoints of sides BC, CA, and AB, respectively. ### Step 2: Use the Midpoint Theorem According to the midpoint theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. ...
Promotional Banner

Topper's Solved these Questions

  • QUADRILATERALS

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|18 Videos
  • QUADRILATERALS

    NCERT EXEMPLAR ENGLISH|Exercise VERY SHORT ANSWER TYPE QUESTIONS|14 Videos
  • POLYNOMIALS

    NCERT EXEMPLAR ENGLISH|Exercise EXERCISE 2.4 Long Answer type Questions|9 Videos
  • STATISTICS AND PROBABILITY

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|12 Videos

Similar Questions

Explore conceptually related problems

In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB of the equilateral DeltaABC. Prove that DeltaDEF is also an equilateral triangle.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: area of BDEF is half the area of Delta ABC.

D,E and F are the middle points of the sides of the triangle ABC, then

In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC . Prove that: (i) square BDEF is a parallelogram (ii) area of Delta DEF = (1)/(4) xx " area of " Delta ABC (iii) square BDEF = (1)/(2) xx " area of " Delta ABC

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles triangle ABC in which AB = BC. Prove that DeltaDEF is also isosceles.

Thevertices of a triangle ABC are A(-7, 8), B (5, 2) and C(11,0) . If D, E, F are the mid-points of the sides BC, CA and AB respectively, show that DeltaABC=4 DeltaDEF .

D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC and G is the centroid of the triangle, then vec(GD) + vec(GE) + vec(GF) =