Home
Class 10
MATHS
D, E and F are respectively the mid-poin...

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

Text Solution

Verified by Experts

The correct Answer is:
`ΔDEF≅ΔEDB≅ΔCFE≅ΔFAD`
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    OSWAAL PUBLICATION|Exercise TEXTBOOK CORNER (EXERCISE 2.5)|17 Videos
  • TRIANGLES

    OSWAAL PUBLICATION|Exercise TEXTBOOK CORNER (EXERCISE 2.6)|10 Videos
  • TRIANGLES

    OSWAAL PUBLICATION|Exercise TEXTBOOK CORNER (EXERCISE 2.3)|16 Videos
  • SURFACE AREA AND VOLUMES

    OSWAAL PUBLICATION|Exercise EXERCISE 15.5|5 Videos

Similar Questions

Explore conceptually related problems

D, E and F are respectively the mid-points of sides AB, BC and CA of Delta ABC . Find the ratio of the areas of Delta DEF and Delta ABC .

D,Eand F are respectively the mid - points of sides AB, BC and CA of DeltaABC . Find the ratio of the areas of DeltaDEF and DeltaABC.

E and F are respectively the mid-points of equal sides AB and AC of DeltaABC (see figure) Show that BF = CE.

If D, E and F are respectively, the mid-points of AB, AC and BC in DeltaABC , then BE + AF is equal to

If D, E and F be the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is

If D, E, F are respectivley the mid points of AB, AC and BC respectively in a triangle ABC, then vec BE + vec AF =

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

D,E and F are respectively the mid-points of the sides BC, CA and AB of triangle ABC show that (i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4 ar (ABC) (iii) ar (BDEF) = 1/2 ar (ABC)

If E,F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) = (1)/(2) ar (ABCD)

If D , E and F are the mid-points of the sides BC , CA and AB respectively of the DeltaABC and O be any point, then prove that OA+OB+OC=OD+OE+OF