Question

In a triangle ABC D is the midpoint of side BC such that BD is equal to half AC show that triangle ABC is a right triangle according to class 9th Maths chapter 7

Answer 1

Answer:

Step-by-step explanation:

In ΔADB, AD = BD

∠DAB = ∠DBA = ∠x ( these are the angles which have opposite sides)

In ΔDCB, BD = CD

∠DBC = ∠DCB = ∠y

In ΔABC we will use the angle sum property

∠ABC + ∠BCA + ∠CAB = 180°

2(∠x + ∠y) = 180°

∠x + ∠y = 90°

∠ABC = 90°

This means that ABC is the right angled triangle.

SO WE HAD PROVED THAT IN A RIGHT ANGLED TRIANGLE ABC , D IS THE MIDPOINT OF SIDE BC SUCH THAT  BD IS EQUAL TO 1/2 AC