Question

Биссектрисы углов P и R параллелограмма OPRS пересекаются на стороне OS. Найди PR, если RS=6. Если в ответе десятичная дробь, то отделите целую часть от дробной с помощью запятой без пробелов.ДАЮ 12 БАЛЛОВ

Answer 1

Ответ:

12

Объяснение:

см.фото

Answer 2

Bisectors of Angles P and R in Parallelogram OPRS

To find the length of PR in parallelogram OPRS, we need to use the information that the bisectors of angles P and R intersect on side OS, and that RS = 6.

Let's analyze the given information step by step.

1. We have a parallelogram OPRS, where O is one vertex and the opposite vertex is S. 2. The bisectors of angles P and R intersect on side OS. 3. RS = 6.

To find the length of PR, we can use the following approach:

1. Let's assume that the point of intersection of the bisectors of angles P and R is point X. 2. Since the bisectors of angles P and R intersect on side OS, we can conclude that point X lies on side OS. 3. Let's denote the length of PX as x and the length of SX as y. 4. Since the bisectors of angles P and R intersect at point X, we can conclude that angles PXO and RXO are equal. 5. Therefore, triangles PXO and RXO are congruent by the angle-angle-side (AAS) congruence criterion. 6. As a result, we can conclude that the lengths of PO and RO are equal, and the lengths of PX and RX are also equal. 7. Let's denote the length of PR as z.

Based on the above information, we can set up the following equations:

1. PX + RX = PR (since PR = PX + RX) 2. PO = RO (since the lengths of PO and RO are equal)

Now, let's solve for the length of PR.

Since triangles PXO and RXO are congruent, we can conclude that the lengths of PX and RX are equal. Let's denote this length as a.

Therefore, we have:

1. PX = a 2. RX = a

Since PO = RO, we can denote this length as b.

Therefore, we have:

1. PO = b 2. RO = b

Using the information that RS = 6, we can conclude that SX = 6.

Therefore, we have:

1. SX = 6

Now, let's substitute these values into the equation PX + RX = PR:

a + a = z

Simplifying the equation, we get:

2a = z

Since PO = RO = b, we can substitute these values into the equation a + b + SX = PX + RX:

a + b + 6 = a + a

Simplifying the equation, we get:

b + 6 = a

Now, let's substitute the value of b + 6 into the equation 2a = z:

2(b + 6) = z

Simplifying the equation, we get:

2b + 12 = z

Therefore, the length of PR is 2b + 12.

Now, let's substitute the value of RS = 6 into the equation b + 6 = a:

b + 6 = 6

Simplifying the equation, we get:

b = 0

Therefore, the length of PR is 2(0) + 12 = 12.

So, PR = 12.

Please let me know if you need any further clarification or assistance!