Book Online Demo
Check Your IQ
Try Test

Courses

Dropper NEET CourseDropper JEE CourseClass - 12 NEET CourseClass - 12 JEE CourseClass - 11 NEET CourseClass - 11 JEE CourseClass - 10 Foundation NEET CourseClass - 10 Foundation JEE CourseClass - 10 CBSE CourseClass - 9 Foundation NEET CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course

Q.

If the 3 altitudes of a triangle are equal, then triangle is:


see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

A scalene triangle

b

An isosceles triangle

c

An equilateral triangle

d

None of these 

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that the three altitudes of the triangle are equal.
So, AD = BF = CE.
Question ImageConsider triangles BEC and BFC  EC=BF   (Equal altitudes)
∠BEC=∠BFC= 90 o   (BE and BF are Altitudes)
BC=BC   (common)
ΔBEC≅ΔBFC   (RHS postulate)
∠ABC=∠BCA   (Corresponding angles)
Also,
Consider the ΔADB   and ΔADC  ,
  ∠ADB=∠ADC= 90 o   (AD is altitude)
AD=AD   (common)
∠ABC = ∠BCA   (proved above)
Thus, △ADB ⩭  △ADB (ASA postulate)
AB=AC   (Corresponding sides are equal)
Similarly, we can prove △BFC ≅ △BFA.
And, hence, BC=AC  .
Thus, AB=AC=BC  .
It implies that if the altitudes of the triangle are equal, then 3 sides of the triangle are also equal. So, the triangle will be an equilateral triangle.
Hence, the correct option is 3.
 
Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
Result Producing online coaching for JEE/NEET of south India
Largest All India Test Series for JEE/NEET
Best Books for IIT JEE
Best Books for NEET
whats app icon