# CD and GH are respectively the bisectors of ∠ ACB and ∠ EGF in such a way that D and H lie on sides AB and FE of Δ ABC and Δ EFG respectively. If Δ ABC ~ Δ FEG, show that:(i) (ii) Δ DCB ~ Δ HGE(iii) Δ DCA ~ Δ HGF

Given, Δ ABC Δ FEG …..eq(1)

corresponding angles of similar triangles

BAC = EFG ….eq(2)

And ABC = FEG …….eq(3)

ACB = FGE

ACD = FGH and BCD = EGH ……eq(4)

Consider Δ ACD and Δ FGH

From eq(2) we have

DAC = HFG

From eq(4) we have

ACD = EGH

If the 2 angle of triangle are equal to the 2 angle of another triangle, then by angle sum property of triangle 3rd angle will also be equal.

by AAA similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar.

By Converse proportionality theorem

Consider Δ DCB and Δ HGE

From eq(3) we have

DBC = HEG

From eq(4) we have

BCD = FGH

Also, BDC = EHG

Δ DCB ΔHGE

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
Champ Quiz | Thales Theorem49 mins
Quiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?36 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
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 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