Question

Точки В и D лежат в разных полуплоскостях относительно прямой АС. Треугольники АВС и ADC — равносторонние. Доказать: АВ || CD. ЧЕРТЁЖ ОБЯЗАТЕЛЬНО ДЛЯ 7-ГО КЛАССА!!!!!!!​

Answer 1

Ответ:

AB=BC=AD=CD, ABCD - ромб, из этого следует, что BC||AD и AB||CD

Answer 2

Given Information:

- Points B and D lie in different half-planes relative to line AC. - Triangles ABC and ADC are equilateral.

To Prove:

- AB || CD.

Proof:

Since triangles ABC and ADC are equilateral, we know that all sides of these triangles are congruent. Therefore, AB = AC = BC and AD = AC = DC.

Now, let's consider the line segment BD. Since points B and D lie in different half-planes relative to line AC, we can conclude that the line segment BD intersects line AC at some point E.

Let's consider triangles ABE and CDE. Since AB = AC and AD = AC, we have AB = AC = AD. Additionally, angle ABE = angle CDE = 60 degrees because triangles ABC and ADC are equilateral.

By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangles ABE and CDE are congruent.

Therefore, AE = CE and BE = DE.

Now, let's consider triangles ABE and CDE. Since AE = CE and BE = DE, we can conclude that these triangles are isosceles.

By the Converse of the Base Angles Theorem, we know that if a triangle is isosceles, then the base angles are congruent.

Therefore, angle AEB = angle CED.

Since angle AEB and angle CED are corresponding angles formed by parallel lines AB and CD intersected by transversal line AC, we can conclude that AB || CD.

Hence, we have proved that AB || CD.

Note: The diagram is not provided, but the proof is based on the given information and the properties of equilateral triangles.