Q. 164.6( 8 Votes )

In Fig., if <span

Answer :

Given: ABBC


DC BC


DE AC


To prove: ΔCED ~ΔABC


Theorem Used:


If two corresponding angles of two triangles are equal the triangles are said to be similar.


Proof:



In ΔABC,


ABC + BAC + BCA = 180° (By angle sum property)


90° + BAC + BCA = 180°


BAC + BCA = 90°……(i)


As DC BC,


BCA + ECD = 90° …… (ii)


Compare equation (i) and (ii)


BAC = ECD …. (iii)


In ΔCED and ΔABC


CED = ABC (Each 90 °)


ECD = BAC (From equation iii)


Then, ΔCED ~ΔABC. (By AA similarity)


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