Question

1. Отрезки АД и ВС пересекаются в точке Е так, что АЕ-ЕД. угол А равен углу Д. Докажите, что треугольник АВЕ равен треугольнику ДСЕ. помогите пж ток чтобы правильно было​

Answer 1

Ответ:

Треугольники равны по 2 признаку равенства треугольников-по стороне и двум прилегающим к ней углам

АЕ=ЕD;<A=<D;по условию задачи

<АЕВ=<СЕD,как вертикальные

Объяснение:

Answer 2

To prove that triangle AVE is congruent to triangle DSE, we can use the Angle-Side-Angle (ASA) congruence criterion. According to the given information, segments AD and VS intersect at point E such that AE = ED, and angle A is equal to angle D.

Proof:

1. Given: AE = ED, angle A = angle D, and segments AD and VS intersect at point E. 2. To prove: Triangle AVE is congruent to triangle DSE.

To prove the congruence of the triangles, we need to show that they have the same three corresponding parts: two sides and the included angle.

Proof of Side AE = Side DE:

Since AE = ED (given), we have one side of triangle AVE equal to one side of triangle DSE.

Proof of Angle A = Angle D:

Since angle A = angle D (given), we have one angle of triangle AVE equal to one angle of triangle DSE.

Now, we need to prove that Side AV = Side DS.

Proof of Side AV = Side DS:

To prove that side AV is equal to side DS, we can use the fact that segments AD and VS intersect at point E.

Consider triangle AED and triangle VES. These triangles share side AE = ED and angle A = angle D. Additionally, segment AV is parallel to segment DS because they are corresponding sides of the transversal ES.

By the Angle-Side-Angle (ASA) congruence criterion, we can conclude that triangle AED is congruent to triangle VES.

Since congruent triangles have corresponding sides equal in length, we can say that side AV is equal to side DS.

Therefore, we have proved that triangle AVE is congruent to triangle DSE using the Angle-Side-Angle (ASA) congruence criterion.

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