Question

15 МИНУТ ДО КОНЦА! В круге проведены диаметры АВ и СD. Докажите, что АС = ВD.

Answer 1

Ответ:

Объяснение:

    Нехай т. О - центр даного кола . У ΔАОС  і  ΔВОD  ∠АОС = ∠ВОD як вертикальні кути , а  ОА = ОВ = r ;  OC = OD = r , тому за  І - ю

ознакою рівності тр - ників  АОС = ΔВОD . Звідси АС = BD .

Доведено .

Answer 2

Given Information

In the given problem, we have a circle with diameters AB and CD. We need to prove that AC is equal to BD.

Proof

To prove that AC is equal to BD, we can use the fact that the diameter of a circle bisects it into two equal halves. Therefore, we can say that AB is equal to CD.

Let's assume that the point of intersection of AB and CD is E. Now, we have two triangles, AEC and BED, which share the side AE and DE.

According to the Side-Side-Side (SSS) congruence criterion, if two triangles have three sides equal in length, then the triangles are congruent.

Since AB is equal to CD, we can say that AE is equal to DE. And since AE is equal to DE, we can say that triangle AEC is congruent to triangle BED.

Now, if two triangles are congruent, then their corresponding sides are equal in length. Therefore, we can say that AC is equal to BD.

Hence, we have proved that AC is equal to BD.

Note: The given problem does not provide specific measurements or angles, so we can only prove the equality of AC and BD based on the fact that AB is equal to CD.