In an isosceles triangle, the median joining the vertex (formed by intersection of equal sides) to the midpoint of the opposite side is an altitude.

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

True

False

answer is A.

(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

in the triangle ΔABC :
AB=AC & ∠B=∠C since ΔABC is isosceles.
BD=CD , since AD is the median and a median divides the side it is projected on in half
Now taking ΔABD and ΔADC
AB=AC
BD=CD
∠B=∠C
Therefore ΔABD and ΔADC are congruent triangles
⇒ΔABD ≅ ΔADC (By Side Angle Side Theorem(SAS))
we can conclude that,
⇒∠ADB=∠ADC (Common parts of Congruent Triangles(CPCT)) .....(i)
BDC is a straight line therefore
∠BDC=180∘
⇒∠ADB+∠ADC = ∠BDC = 180∘
Substituting equation (i) in the above equation, we get
⇒2∠ADB=180∘
⇒∠ADB=90∘
⇒∠ADB=∠ADC=90∘
An altitude is a line that makes an angle of ∠90∘ with the line it is projected on, therefore it is proved that ADAD is the altitude of the isosceles triangle ΔABC

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

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

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

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