Question

∆ABC is isosceles in which AB = AC. Seg BD and seg CE are medians. 

Show that BD = CE.

Given: In isosceles ∆ABC, AB = AC. seg BD and seg CE are the medians of ∆ABC. 

To prove: BD = CE

Answer 1

To prove: BD = CE 

Proof: AE = \(\frac1{2}\)AB …..(i) [E is the midpoint of side AB] 

AD = \(\frac1{2}\)AC ….(ii) [D is the midpoint of side AC] 

Also, AB = AC ……(iii) [Given] 

∴ AE = AD ….(iv) [From (i), (ii) and (iii)] 

In ∆ADB and ∆AEC,

seg AB ≅ seg AC ∠BAD ≅ ∠CAE

 seg AD ≅ seg AE

∴ ∆ADB ≅ ∆AEC

 ∴ seg BD ≅ seg CE 

∴ BD = CE