In the parallelogram ABCD AC = 15 cm The middle M of the side AB is connected by a segment

| September 16, 2021 | education

In the parallelogram ABCD AC = 15 cm The middle M of the side AB is connected by a segment to the vertex D. Find the segments into which the DM divides the diagonal AC.

Let us also draw the diagonal BD of the parallelogram ABCD.

By the property of the diagonals, they are divided in half at the point of their intersection, then BO1 = DO1, AO1 = CO1 = AC / 2 = 15/2 = 7.5 cm.

Consider a triangle ABD, in which the segments AO1 and D have medians, since they divide the opposite sides in half.

By the property of the medians of the triangle, they are divided at the point O in a ratio of 2/1 starting from the vertex.

Then AO = 2 * OO1.

AO + OO1 = 2 * OO1 + OO1 = 3 * OO1 = AC / 2 = 7.5 cm.

OO1 = 7.5 / 3 = 2.5 cm.

AO = 2.5 * 2 = 5 cm.

CO = AC – AO = 15 – 5 = 10 cm.

Answer: DM divides the speaker into 5 cm and 10 cm segments.



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