Question

if the hypotenuse AC Of a right angle triangle abc is of lenght 2ab prove angle BAC is equal to 2angle acb​

Answer 1

Answer:

Step-by-step explanation:

Using angle sum property of triangle ABC

∠ABC + ∠BAC + ∠ACB = 180°

⇒ 90° + ∠BAC + 2∠BAC = 180°

⇒ 3∠BAC = 90°

⇒∠BAC = 30°

∴ ∠ACB = 2 × 30° = 60°

Similarly, it can be proved that ∠ADB = 60° and ∠BAD = 30°

∴ ∠CAD = 30° + 30° = 60°

In ∆ACD, ∠CAD = ∠ACD = ∠ADC = 60°

So, ∆ABC is an equilateral triangle.

∴ AC = CD = AD

we know that the perpendicular drawn to a side from opposite vertex bisects the side

∴ CD = 2BC

⇒ AC = 2BC [CD = AC]

Hence, proved