Question

Знайдіть довжину відрізків АО і ВО паралелограма АВСК, якщо його діагоналі дорівнюють 24 дм і 30 дм, а точка О – точка перетину діагоналей

Answer 1

Ответ:

12 дм та 15 дм

Объяснение:

За ознакою паралелограма точка О дiлить дiагоналi навпiл, отож середини дiагоналей дорiвнюють 12 дм та 15 дм.

Answer 2

Ответ:

Объяснение:

В параллелограмме точка пересечения диагоналей делит их пополам.

АС = 30см  → АО = ОС = 30/2 = 15 (см)

ВК = 24см   → ВО = ОК = 24/2 = 12(см)

Answer 3

Finding the Length of Segments AO and BO in Parallelogram ABCD

To find the length of segments AO and BO in parallelogram ABCD, we can use the properties of diagonals in a parallelogram.

Given: - Length of one diagonal AC = 24 dm - Length of the other diagonal BD = 30 dm - Point O is the point of intersection of the diagonals

Solution:

In a parallelogram, the diagonals bisect each other. This means that they divide each other into two equal parts.

Let's denote the length of segments AO and BO as x and y, respectively.

According to the properties of diagonals in a parallelogram: - AO = CO - BO = DO

We can use the given lengths of the diagonals to form equations to solve for x and y.

From the given information: - AC = 24 dm - BD = 30 dm

Using the properties of diagonals in a parallelogram, we can set up the following equations: - AO + CO = AC - BO + DO = BD

Substituting the values: - x + x = 24 - y + y = 30

Solving the equations: - 2x = 24 - 2y = 30

Dividing by 2: - x = 12 - y = 15

Answer:

The length of segment AO is 12 dm, and the length of segment BO is 15 dm.