Q. 134.0( 2 Votes )

Two isosceles 9

Answer :

Given: ΔABC and ΔPQR are isosceles and ∠A = ∠P. AD, PS are the altitudes and .
To find: AD
          PS
Proof: In Δ ABC, ∠B = ∠C (isosceles Δ property) Similarly in Δ PQR, ∠Q = ∠R.
                  ∠A = ∠P (given)∴ ∠B = ∠C =
Since ∠ A = ∠ P 
∠ B = ∠ C = ∠ Q = ∠R 
∴ Δ ABC ~ Δ PQR (AA)
If 2 triangles are similar then the ratio of areas will be equal to the square of the corresponding sides,  
…………………(1)
In Δ ABD, Δ PQS
∠D = ∠S (= 90° )
∠B = ∠Q (given)
∴ Δ ABD ~ Δ PQS (AA)
∴  AB = AD  ……………….(2) 
  PQ    PS
According equation (1)
 
AD  =  3
   PS     4
... The ratio of their corresponding heights is 3 : 4.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
view all courses
RELATED QUESTIONS :

Draw the graph ofNCERT - Mathematics