The diagonal divides the middle line of the trapezoid into 4 and 13 cm segments. Find the bases of the trapezoid.

univerkov | August 8, 2021 | education

Consider a triangle ABC.

Point M is the middle of side AB, since MR is the middle line of the trapezoid, BC is parallel to MO, therefore, the segment MO is the midline of triangle ABC, the length of which is equal to half the length of the base, which is parallel to it.

MO = BC / 2.

BC = 2 * MO = 2 * 4 = 8 cm.

Consider triangle ACD.

Point P is the middle of the side CD, since MP is the middle line of the rapezoid, AD is parallel to PO, therefore, the segment PO is the midline of the triangle ACD, the length of which is half the length of the base, which is parallel to it.

PO = AD / 2.

AD = 2 * РO = 2 * 13 = 26 cm.

Answer: The bases of the trapezoid are 8 cm and 26 cm.

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.