Check sibling questions

Example 7 - In ABC, D, E and F are mid-points of sides - Examples

Example 7 - Chapter 8 Class 9 Quadrilaterals - Part 2
Example 7 - Chapter 8 Class 9 Quadrilaterals - Part 3

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

Example 7 In Δ ABC, D, E and F are respectively the mid-points of sides AB, BC and CA . Show that Δ ABC is divided into four congruent triangles by joining D, E and F. 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 ∴ DF ∥ BC 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 Similarly, DFCE is a parallelogram, ∴ Δ DFE ≅ Δ CEF ADEF is also parallelograms, ∴ Δ ADF ≅ Δ DFE From (1), (2) & (3) Δ DBE ≅ Δ DFE ≅ Δ CEF ≅ Δ ADF ∴ All 4 triangles are congruent

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.