Question

In quadrilateral ABCD , AB=AC=AD,then prove that angle BAD=2(angle BDC+angle CBD

Answer 1

Step-by-step explanation:

Given In quadrilateral ABCD , AB=AC=AD,then prove that angle BAD=2(angle BDC+angle CBD  

• Consider a quadrilateral ABCD  
• So AB = AC = AD
• Join AC and BD
• Now from Angle sum property of quadrilaterals we get
• 360 – B – C – D = BAD
• Since the triangles ABC and ACD are isosceles
• Now B = ACB and D = ACD
• So 360 – ACD – C – ACB = BAD
• Now C = ACB + ACD
• Now 360 – 2ACB – 2ACD = BAD
•      2 x 180 – 2(ACB + ACD) = BAD
•       2 (180 – C ) = BAD
• Now angle sum property of triangles.
•        Now 180 – C = BDC + CBD
• Therefore BAD = 2 (angle CDB + angle CBD)

Reference link will be

https://brainly.in/question/14717255