Question

3.Отрезки АВ и CD равны и пересекаются в точке О так, АО = OD. Докажите, что BD = АС.

Answer 1

Если это треугольники:

Дано:

Отрезки AB, CD

AO=OD

Доказать:

BD = AC

Решение:

1.АВ=СД(по усл),АО=СД(по усл) => СО=ОВ

2.АВ=СД(по усл) СО=ОВ(по доказ.), => АОС=ДОВ(по первому признаку) => АС=ДВ

ЧТД

Answer 2

АВ=СD ( по условию) , АО=СD ( тоже по услов.) следовательно СО=ОВ

потом

AB=CD ( по услов) углы AOC=BOD (т.к вертикальные) СО=ОВ из этого следует .что треугольники AOC=BOD ( по первому признаку равенства) раз треугольники равны, следовательно ВD=AC

Answer 3

Given Information:

We are given that segments AB and CD are equal in length and intersect at point O, and that AO is equal to OD. We need to prove that BD is equal to AC.

Proof:

To prove that BD is equal to AC, we can use the given information and apply the properties of congruent triangles.

1. Given: AB = CD and AO = OD. 2. Since AO = OD, we can conclude that triangle AOD is an isosceles triangle. 3. By the properties of isosceles triangles, we know that the base angles of triangle AOD are congruent. 4. Let's denote the measure of angle AOD as x. 5. Since the base angles of triangle AOD are congruent, we can conclude that angle ADO is also x degrees. 6. Similarly, angle ADO is also x degrees. 7. Now, let's consider triangle ABD and triangle AOC. 8. Angle ABD is equal to angle ADO (both are x degrees) and angle AOC is equal to angle ADO (both are x degrees). 9. Therefore, angle ABD is congruent to angle AOC. 10. By the Angle-Angle (AA) postulate, we can conclude that triangle ABD is congruent to triangle AOC. 11. By the definition of congruent triangles, we know that corresponding sides of congruent triangles are equal in length. 12. Therefore, BD is equal to AC.

Hence, we have proved that BD is equal to AC.