In parallelogram ABCD, the diagonals intersect at point O. The adjacent sides of the parallelogram

univerkov | August 16, 2021 | education

In parallelogram ABCD, the diagonals intersect at point O. The adjacent sides of the parallelogram are 10 cm and 15 cm. Find the difference between the perimeters of triangles AOB and AOD.

1. Adjacent sides AB = 10 cm, BC = 15 cm.

2. The sum of the sides of the triangle AOB = AB + BO + AO.

3. The sum of the sides of the triangle AOD = AD + AO + OD.

4. Opposite sides of the parallelogram BC = AD = 15 cm. BO = OD, since the intersecting diagonals are divided into two equal segments.

5. Replacing OD by ВO in the second expression, calculate the difference between the perimeters of the triangle AOD and AOB:

(AD + AO + BO) – (AB + BO + AO) = 15 – 10 = 5 cm.

Answer: the perimeter of triangle AOD is 5 cm larger than the perimeter of triangle AOB.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.