Question

Помогите пожалуйста!(геометрия).Луч SC является биссектрисой угла ASB. а отрезки SA и SB равны. Докажите, что треугольник SAC=треугольникуSBC. Если пришлёте ответ решённый на листочке и отправленный сюда буду в тройне благодарна.

Answer 1

....................

Answer 2

To prove that triangle SAC is congruent to triangle SBC, we can use the Angle-Side-Angle (ASA) congruence criterion. According to the given information, the ray SC is the angle bisector of angle ASB, and the segments SA and SB are equal in length.

Proof:

1. Given: Ray SC is the angle bisector of angle ASB, and SA = SB. 2. To prove: Triangle SAC ≅ Triangle SBC.

To prove the congruence, we need to show that the corresponding angles and sides of the two triangles are congruent.

Proof of Angle Congruence:

Since ray SC is the angle bisector of angle ASB, it divides the angle into two congruent angles. Let's call these angles x.

- Angle SAC: This angle is formed by the ray SA and the ray SC. It is equal to angle x. - Angle SBC: This angle is formed by the ray SB and the ray SC. It is also equal to angle x.

Therefore, angle SAC is congruent to angle SBC.

Proof of Side Congruence:

Since SA = SB, the two sides are equal in length.

Therefore, side SA is congruent to side SB.

Conclusion:

By the ASA congruence criterion, we have shown that angle SAC is congruent to angle SBC, and side SA is congruent to side SB. Therefore, triangle SAC is congruent to triangle SBC.

I hope this explanation helps! Let me know if you have any further questions.