Question

Отрезки AB и CD есть параллельными и ровными докажите что треугольник ABC =треугольник DCB, если отрезки AD и BC пересикаются

Answer 1

Ответ:

Объяснение:

AB II CD

углы ABC=BCD, BAC=BDC как накрестлежащие

AB=CD

следовательно тр-ки ABC=DCB по признаку равенства (угол-сторона-угол)

Answer 2

#### Proof that Triangle ABC is congruent to Triangle DCB To prove that Triangle ABC is congruent to Triangle DCB, given that segments AB and CD are parallel and equal, and segments AD and BC intersect, we can use the Side-Angle-Side (SAS) congruence criterion. **Step 1: Establish that AB is parallel to CD and AB is equal to CD.** Given that segments AB and CD are parallel and equal, we can conclude that AB and CD are corresponding sides of two parallel lines. This means that AB and CD have the same length and are parallel to each other. **Step 2: Establish that AD and BC intersect.** Given that segments AD and BC intersect, we can conclude that there is a point of intersection between these two segments. **Step 3: Identify the common side.** The common side between Triangle ABC and Triangle DCB is segment BC. **Step 4: Identify the congruent sides.** We have established that AB is equal to CD. Additionally, since AB is parallel to CD, we can conclude that segment AD is equal to segment BC. This is because corresponding sides of two parallel lines are equal. **Step 5: Identify the congruent angles.** We do not have any information about the angles in the given question. Therefore, we cannot establish any congruent angles between Triangle ABC and Triangle DCB. **Step 6: Apply the SAS congruence criterion.** Using the SAS congruence criterion, we can conclude that Triangle ABC is congruent to Triangle DCB if the following conditions are met: - The common side BC is equal in both triangles. - The side AB is equal to the corresponding side CD. Since both conditions are met, we can conclude that Triangle ABC is congruent to Triangle DCB. Please note that without additional information about the angles or other sides of the triangles, we cannot establish complete congruence between the two triangles.