Question

Всередині рівностороннього трикутника взято точку О ,яка сполучена з усіма вершинами трикутника.Знайти рівні трикутники,якщо кут ОВС дорівнює кутк ВСО​

Answer 1

Ответ:

ΔACO=ΔABO

Объяснение:

ΔABC-равносторонний, ∠OBC =∠BCO​

ΔABC-равносторонний⇒AB=AC, ∠B=∠C

∠ACO=∠C-∠BCO=∠B-∠OBC=∠ABO⇒∠ACO=∠ABO

∠OBC =∠BCO​⇒ΔOBC-равнобедренный⇒OB=OC

OB=OC, ∠ACO=∠ABO, AC=AB⇒ΔACO=ΔABO по двум сторонам и углу между ними, 1-ый признак равенства треугольников.

Answer 2

Given Information:

We are given that point O is taken inside an equilateral triangle and is connected to all three vertices of the triangle. We need to find the congruent triangles if angle OVS is equal to angle VSO.

Solution:

To find the congruent triangles, we need to determine the relationship between the sides and angles of the triangles. Let's analyze the given information and use some geometric properties.

1. Equilateral Triangle: - An equilateral triangle has three equal sides and three equal angles. - Each angle in an equilateral triangle measures 60 degrees.

2. Triangle OVS: - Triangle OVS is formed by connecting point O to vertices V and S of the equilateral triangle. - We are given that angle OVS is equal to angle VSO.

To find the congruent triangles, we need to determine the relationship between the sides and angles of triangles OVS and VSO.

Relationship between Triangles OVS and VSO:

Since angle OVS is equal to angle VSO, we can conclude that triangles OVS and VSO are congruent by the Angle-Side-Angle (ASA) congruence criterion.

The ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

In this case, angle OVS is congruent to angle VSO, and side OV is common to both triangles. Therefore, triangles OVS and VSO are congruent.

Conclusion:

Triangles OVS and VSO are congruent.