Question

IN triangle ABC, D is the midpoint of side AC such that BD =half of AC. Show
that ABC is a right angle.
​

Answer 1

Answer:

Rainforests are forests characterized by high and continuous rainfall, with annual rainfall in the case of tropical rainforests between 2.5 and 4.5 metres and definitions varying by region for temperate rainforests.

Answer 2

From the figure we know that D is the midpoint of the line AC

So..

AD = CD = ½ AC

BD = ½ AC. [Given]

AD = BD = CD

• Let us consider AD = BD

∠ BAD = ∠ ABD …..(1) [the angles opposite to equal sides are equal]

• Let us consider CD = BD

∠ BCD = ∠ CBD ….. (2) [the angles opposite to equal sides are equal]

in △ ABC

∠ ABC + ∠ BAC + ∠ BCA = 180 [angle sum property]

we can write

∠ ABC + ∠ BAD + ∠ BCD = 180

we get ∠ ABC + ∠ ABD + ∠ CBD = 180 [ By using equation (1) and (2)]

∠ ABC + ∠ ABC = 180o [By addition 2]

∠ABC = 180 By division ∠ABC = 90o

Therefore, ∠ABC is a right