In trapezoid ABCD AC-bisector of angle A divides the trapezoid into two similar triangles ABCD

univerkov | June 25, 2021 | education

In trapezoid ABCD AC-bisector of angle A divides the trapezoid into two similar triangles ABCD and ACD, AB = 9cm, CD = 12cm. Find the perimeter of the trapezoid.

Since AC is the bisector of angle A, then the angle BAC = CAD, and the angle BCA = CAD, as the angles lying crosswise, then the angle BAC = BCA, and therefore the triangle ABC is isosceles, AB = BC = 9 cm.
Triangles ABC and ACD are similar in condition, and triangle ABC is isosceles, then triangle ACD will be isosceles and AC = CD = 12 cm.
Then AD / AC = CD / BC.
AD = AC * CD / BC = 12 * 12/9 = 144/9 = 16 cm.
Let’s calculate the perimeter of the trapezoid. Ravsd = AB + BC + CD + AD = 9 + 9 + 12 + 16 = 46 cm.
Answer: The perimeter of the trapezoid is 46 cm.

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