Q. 205.0( 1 Vote )

In a , perpendicular AD from A on BC meets BC at D. If BD = 8 cm, DC = 2 cm and AD = 4 cm, thenA. is isoscelesB. is equilateralC. AC = 2 ABD. is right-angled at A.

Given in ΔABC, AD BC, BD = 8 cm, DC = 2 cm and AD = 4 cm.

We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AC2 = (4)2 + (2)2

= 16 + 4

AC2 = 20 … (1)

AB2 = AD2 + BD2 = 42 + 82 = 16 + 64

AB2 = 80 … (2)

Now, in ΔABC,

BC2 = (CD + DB)2 = (2 + 8)2 = 102 = 100

And AB2 + CA2 = 80 + 20 = 100

AB2 + CA2 = BC2

Hence, ΔABC is right angled at A.

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
A Peep into Pythagoras Theorem43 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
Quiz | Criterion of Similarity of Triangle45 mins
How to Ace Maths in NTSE 2020?36 mins
Champ Quiz | Thales Theorem49 mins
NCERT | Concept Based Questions on Triangles31 mins
Know About Important Proofs in Triangles33 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