The diagonals of the rectangle ABCD meet at the point O. a) prove that the triangles AOD and AOB are isosceles.

| November 23, 2020 | education

The diagonals of the rectangle ABCD meet at the point O. a) prove that the triangles AOD and AOB are isosceles. b) Find the perimeter of triangle AOB if CAD = 30 degrees, AC = 12 cm.

Rectangle Diagonals Property – The diagonals are equal and are halved at the intersection. Therefore, the triangles are isosceles, since their 2 sides are equal. Perimeter is the sum of all sides. From the property of the diagonals, the side ao = half of the diagonal = 6 cm. Since the triangle is isosceles, the side ob = 6 cm. Consider the triangle acd. Angle cad = 30 degrees, this triangle is rectangular, angle d = 90. The side of a right-angled triangle opposite an angle of 30 degrees = half of the hypotenuse, therefore cd = 6 cm. Сd = ab, therefore the perimeter of the triangle = 6 + 6 + 6 = 18 cm
Answer: 18 cm



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