# In the given figure, DEFG is a square and ∠BAC is a right angle. Show that DE2= BD x EC. Given: DEFG is a square and BAC = 90°

To Prove: DE2 = BD × EC.

In AGF and DBG

GAF = BDG [each 90°]

AGF = DBG

[corresponding angles because GF|| BC and AB is the transversal] AFG ~ DBG [by AA Similarity Criterion] …(1)

In AGF and EFC

GAF = CEF [each 90°]

AFG = ECF

[corresponding angles because GF|| BC and AC is the transversal] AGF ~ EFC [by AA Similarity Criterion] …(2)

From equation (1) and (2), we have DBG ~ EFC

Since, the triangle is similar. Hence corresponding sides are proportional  [DEFG is a square]

DE2 = BD × EC

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Basic Proportionality Theorem42 mins  A Peep into Pythagoras Theorem43 mins  NCERT | Strong Your Basics of Triangles39 mins  RD Sharma | Imp. Qs From Triangles41 mins  R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class  Quiz | Criterion of Similarity of Triangle45 mins  How to Ace Maths in NTSE 2020?36 mins  Know About Important Proofs in Triangles33 mins  Master BPT or Thales Theorem39 mins  R.D Sharma | Solve Exercise-4.545 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 