Question

Три точки P , Q, R лежат на одной прямой . Известно , что PR=2,1 см , QR=в три раза больше отрезка PR , PQ=8,4 см. Докажите, что точка R лежит между точками P и Q ПОМОГИТЕ ! ДАЮ 15 баллов! ГЕОМЕТРИЯ 7 КЛАСС

Answer 1

Среди любых трех точек, лежащих на одной прямой, только одна лежит между двумя другими.

Если точка R лежит между точками P и Q, то выполняется равенство PR+RQ=PQ.

PR+RQ=PQ <=> 4*PR=PQ <=> 4*2,1 =8,4

Равенство выполняется, тем самым доказано, что точка R лежит между точками P и Q.

Answer 2

Given Information:

We are given three points P, Q, and R that lie on the same line. The lengths of the line segments are as follows: - PR = 2.1 cm - QR is three times the length of PR - PQ = 8.4 cm

To Prove:

We need to prove that point R lies between points P and Q.

Solution:

To prove that point R lies between points P and Q, we need to show that PR + RQ = PQ.

Given that PR = 2.1 cm and QR is three times the length of PR, we can calculate the length of QR as follows: QR = 3 * PR = 3 * 2.1 cm = 6.3 cm.

Now, let's calculate the sum of PR and RQ: PR + RQ = 2.1 cm + 6.3 cm = 8.4 cm.

Comparing the sum of PR and RQ with the length of PQ, we find that they are equal: PR + RQ = PQ = 8.4 cm.

Since PR + RQ = PQ, we can conclude that point R lies between points P and Q.

Therefore, we have proven that point R lies between points P and Q.

Note: The given problem does not require any external sources for verification, as it can be solved using basic geometric principles.